Daily Papers

While the uncertainty in generation and demand increases, accurately estimating the dynamic characteristics of power systems becomes crucial for employing the appropriate control actions to maintain their stability. In our previous work, we have shown that Bayesian Physics-informed Neural Networks (BPINNs) outperform conventional system identification methods in identifying the power system dynamic behavior under measurement noise. This paper takes the next natural step and addresses the more significant challenge, exploring how BPINN perform in estimating power system dynamics under increasing uncertainty from many Inverter-based Resources (IBRs) connected to the grid. These introduce a different type of uncertainty, compared to noisy measurements. The BPINN combines the advantages of Physics-informed Neural Networks (PINNs), such as inverse problem applicability, with Bayesian approaches for uncertainty quantification. We explore the BPINN performance on a wide range of systems, starting from a single machine infinite bus (SMIB) system and 3-bus system to extract important insights, to the 14-bus CIGRE distribution grid, and the large IEEE 118-bus system. We also investigate approaches that can accelerate the BPINN training, such as pretraining and transfer learning. Throughout this paper, we show that in presence of uncertainty, the BPINN achieves orders of magnitude lower errors than the widely popular method for system identification SINDy and significantly lower errors than PINN, while transfer learning helps reduce training time by up to 80 %.

State estimation is highly critical for accurately observing the dynamic behavior of the power grids and minimizing risks from cyber threats. However, existing state estimation methods encounter challenges in accurately capturing power system dynamics, primarily because of limitations in encoding the grid topology and sparse measurements. This paper proposes a physics-informed graphical learning state estimation method to address these limitations by leveraging both domain physical knowledge and a graph neural network (GNN). We employ a GNN architecture that can handle the graph-structured data of power systems more effectively than traditional data-driven methods. The physics-based knowledge is constructed from the branch current formulation, making the approach adaptable to both transmission and distribution systems. The validation results of three IEEE test systems show that the proposed method can achieve lower mean square error more than 20% than the conventional methods.

Modern power systems require fast and accurate dynamic simulations for stability assessment, digital twins, and real-time control, but classical ODE solvers are often too slow for large-scale or online applications. We propose a neural-operator framework for surrogate modeling of power system components, using Deep Operator Networks (DeepONets) to learn mappings from system states and time-varying inputs to full trajectories without step-by-step integration. To enhance generalization and data efficiency, we introduce Physics-Informed DeepONets (PI-DeepONets), which embed the residuals of governing equations into the training loss. Our results show that DeepONets, and especially PI-DeepONets, achieve accurate predictions under diverse scenarios, providing over 30 times speedup compared to high-order ODE solvers. Benchmarking against Physics-Informed Neural Networks (PINNs) highlights superior stability and scalability. Our results demonstrate neural operators as a promising path toward real-time, physics-aware simulation of power system dynamics.

We explore the possibility to use physics-informed neural networks to drastically accelerate the solution of ordinary differential-algebraic equations that govern the power system dynamics. When it comes to transient stability assessment, the traditionally applied methods either carry a significant computational burden, require model simplifications, or use overly conservative surrogate models. Conventional neural networks can circumvent these limitations but are faced with high demand of high-quality training datasets, while they ignore the underlying governing equations. Physics-informed neural networks are different: they incorporate the power system differential algebraic equations directly into the neural network training and drastically reduce the need for training data. This paper takes a deep dive into the performance of physics-informed neural networks for power system transient stability assessment. Introducing a new neural network training procedure to facilitate a thorough comparison, we explore how physics-informed neural networks compare with conventional differential-algebraic solvers and classical neural networks in terms of computation time, requirements in data, and prediction accuracy. We illustrate the findings on the Kundur two-area system, and assess the opportunities and challenges of physics-informed neural networks to serve as a transient stability analysis tool, highlighting possible pathways to further develop this method.

Time-domain simulations are crucial for ensuring power system stability and avoiding critical scenarios that could lead to blackouts. The next-generation power systems require a significant increase in the computational cost and complexity of these simulations due to additional degrees of uncertainty, non-linearity and states. Physics-Informed Neural Networks (PINN) have been shown to accelerate single-component simulations by several orders of magnitude. However, their application to current time-domain simulation solvers has been particularly challenging since the system's dynamics depend on multiple components. Using a new training formulation, this paper introduces the first natural step to integrate PINNs into multi-component time-domain simulations. We propose PINNs as an alternative to other classical numerical methods for individual components. Once trained, these neural networks approximate component dynamics more accurately for longer time steps. Formulated as an implicit and consistent method with the transient simulation workflow, PINNs speed up simulation time by significantly increasing the time steps used. For explanation clarity, we demonstrate the training, integration, and simulation framework for several combinations of PINNs and numerical solution methods using the IEEE 9-bus system, although the method applies equally well to any power system size.

This paper introduces a novel learning-based Stochastic Hybrid System (LSHS) approach for detecting and classifying various contingencies in modern power systems. Specifically, the proposed method is capable of identifying hidden contingencies that cannot be captured by existing sensing and monitoring systems, such as failures in protection systems or line outages in distribution networks. The LSHS approach detects contingencies by analyzing system outputs and behaviors. It then categorizes them based on their impact on the SHS model into physical, control network, and measurement contingencies. The stochastic hybrid system (SHS) model is further extended into an advanced closed-loop framework incorporating both system dynamics and observer-based state estimation error dynamics. Machine learning methods within the LSHS framework are employed for contingency classification and rapid detection. The practicality and effectiveness of the proposed methodology are validated through simulations on an enhanced IEEE-33 bus system. The results demonstrate that the LSHS framework significantly improves the accuracy and speed of contingency detection compared to state-of-the-art methods, offering a promising solution for enhancing power system contingency detection.

A common pipeline in learning-based control is to iteratively estimate a model of system dynamics, and apply a trajectory optimization algorithm - e.g.~iLQR - on the learned model to minimize a target cost. This paper conducts a rigorous analysis of a simplified variant of this strategy for general nonlinear systems. We analyze an algorithm which iterates between estimating local linear models of nonlinear system dynamics and performing iLQR-like policy updates. We demonstrate that this algorithm attains sample complexity polynomial in relevant problem parameters, and, by synthesizing locally stabilizing gains, overcomes exponential dependence in problem horizon. Experimental results validate the performance of our algorithm, and compare to natural deep-learning baselines.

Time domain simulation, i.e., modeling the system's evolution over time, is a crucial tool for studying and enhancing power system stability and dynamic performance. However, these simulations become computationally intractable for renewable-penetrated grids, due to the small simulation time step required to capture renewable energy resources' ultra-fast dynamic phenomena in the range of 1-50 microseconds. This creates a critical need for solutions that are both fast and scalable, posing a major barrier for the stable integration of renewable energy resources and thus climate change mitigation. This paper explores operator learning, a family of machine learning methods that learn mappings between functions, as a surrogate model for these costly simulations. The paper investigates, for the first time, the fundamental concept of simulation time step-invariance, which enables models trained on coarse time steps to generalize to fine-resolution dynamics. Three operator learning methods are benchmarked on a simple test system that, while not incorporating practical complexities of renewable-penetrated grids, serves as a first proof-of-concept to demonstrate the viability of time step-invariance. Models are evaluated on (i) zero-shot super-resolution, where training is performed on a coarse simulation time step and inference is performed at super-resolution, and (ii) generalization between stable and unstable dynamic regimes. This work addresses a key challenge in the integration of renewable energy for the mitigation of climate change by benchmarking operator learning methods to model physical systems.

Public power-system datasets often lack electromagnetic transient (EMT) waveforms, inverter control dynamics, and diverse disturbance coverage, which limits their usefulness for training surrogate models and studying cyber-physical behavior in inverter-based microgrids. This paper presents a high-fidelity digital twin dataset generated from a MATLAB/Simulink EMT model of a low-voltage AC microgrid with ten inverter-based distributed generators. The dataset records synchronized three-phase PCC voltages and currents, per-DG active power, reactive power, and frequency, together with embedded scenario labels, producing 38 aligned channels sampled at Δt = 2~μs over T = 1~s (N = 500{,}001 samples) per scenario. Eleven operating and disturbance scenarios are included: normal operation, load step, voltage sag (temporary three-phase fault), load ramp, frequency ramp, DG trip, tie-line trip, reactive power step, single-line-to-ground faults, measurement noise injection, and communication delay. To ensure numerical stability without altering sequence length, invalid samples (NaN, Inf, and extreme outliers) are repaired using linear interpolation. Each scenario is further validated using system-level evidence from mean frequency, PCC voltage magnitude, total active power, voltage unbalance, and zero-sequence current to confirm physical observability and correct timing. The resulting dataset provides a consistent, labeled EMT benchmark for surrogate modeling, disturbance classification, robustness testing under noise and delay, and cyber-physical resilience analysis in inverter-dominated microgrids. The dataset and processing scripts will be released upon acceptance

This paper explores the expressive power of deep neural networks through the framework of function compositions. We demonstrate that the repeated compositions of a single fixed-size ReLU network exhibit surprising expressive power, despite the limited expressive capabilities of the individual network itself. Specifically, we prove by construction that L_2circ g^{circ r}circ mathcal{L}_1 can approximate 1-Lipschitz continuous functions on [0,1]^d with an error O(r^{-1/d}), where g is realized by a fixed-size ReLU network, mathcal{L}_1 and L_2 are two affine linear maps matching the dimensions, and g^{circ r} denotes the r-times composition of g. Furthermore, we extend such a result to generic continuous functions on [0,1]^d with the approximation error characterized by the modulus of continuity. Our results reveal that a continuous-depth network generated via a dynamical system has immense approximation power even if its dynamics function is time-independent and realized by a fixed-size ReLU network.

Large Language Model (LLM) multi-agent systems are increasingly deployed as interacting agent societies, yet scaling these systems often yields diminishing or unstable returns, the causes of which remain poorly understood. We present the first large-scale empirical study of coordination dynamics in LLM-based multi-agent systems, introducing an atomic event-level formulation that reconstructs reasoning as cascades of coordination. Analyzing over 1.5 Million interactions across tasks, topologies, and scales, we uncover three coupled laws: coordination follows heavy-tailed cascades, concentrates via preferential attachment into intellectual elites, and produces increasingly frequent extreme events as system size grows. We show that these effects are coupled through a single structural mechanism: an integration bottleneck, in which coordination expansion scales with system size while consolidation does not, producing large but weakly integrated reasoning processes. To test this mechanism, we introduce Deficit-Triggered Integration (DTI), which selectively increases integration under imbalance. DTI improves performance precisely where coordination fails, without suppressing large-scale reasoning. Together, our results establish quantitative laws of collective cognition and identify coordination structure as a fundamental, previously unmeasured axis for understanding and improving scalable multi-agent intelligence.

We introduce a semidefinite programming algorithm to find the minimal quantum Fisher information compatible with an arbitrary dataset of mean values. This certification task allows one to quantify the resource content of a quantum system for metrology applications without complete knowledge of the quantum state. We implement the algorithm to study quantum spin ensembles. We first focus on Dicke states, where our findings challenge and complement previous results in the literature. We then investigate states generated during the one-axis twisting dynamics, where in particular we find that the metrological power of the so-called multi-headed cat states can be certified using simple collective spin observables, such as fourth-order moments for small systems, and parity measurements for arbitrary system sizes.

Deep learning (DL) algorithms have been widely applied to short-term voltage stability (STVS) assessment in power systems. However, transferring the knowledge learned in one power grid to other power grids with topology changes is still a challenging task. This paper proposed a transferable DL-based model for STVS assessment by constructing the topology-aware voltage dynamic features from raw PMU data. Since the reactive power flow and grid topology are essential to voltage stability, the topology-aware and physics-informed voltage dynamic features are utilized to effectively represent the topological and temporal patterns from post-disturbance system dynamic trajectories. The proposed DL-based STVS assessment model is tested under random operating conditions on the New England 39-bus system. It has 99.99\% classification accuracy of the short-term voltage stability status using the topology-aware and physics-informed voltage dynamic features. In addition to high accuracy, the experiments show good adaptability to PMU errors. Moreover, The proposed STVS assessment method has outstanding performance on new grid topologies after fine-tuning. In particular, the highest accuracy reaches 99.68\% in evaluation, which demonstrates a good knowledge transfer ability of the proposed model for power grid topology change.

The integration of experimental technologies with large language models (LLMs) is transforming scientific research. It positions AI as a versatile research assistant rather than a mere problem-solving tool. In the field of power systems, however, managing simulations -- one of the essential experimental technologies -- remains a challenge for LLMs due to their limited domain-specific knowledge, restricted reasoning capabilities, and imprecise handling of simulation parameters. To address these limitations, this paper proposes a feedback-driven, multi-agent framework. It incorporates three proposed modules: an enhanced retrieval-augmented generation (RAG) module, an improved reasoning module, and a dynamic environmental acting module with an error-feedback mechanism. Validated on 69 diverse tasks from Daline and MATPOWER, this framework achieves success rates of 93.13% and 96.85%, respectively. It significantly outperforms ChatGPT 4o, o1-preview, and the fine-tuned GPT-4o, which all achieved a success rate lower than 30% on complex tasks. Additionally, the proposed framework also supports rapid, cost-effective task execution, completing each simulation in approximately 30 seconds at an average cost of 0.014 USD for tokens. Overall, this adaptable framework lays a foundation for developing intelligent LLM-based assistants for human researchers, facilitating power system research and beyond.

The rapid integration of renewable energy sources is transforming modern electric power systems into converter-dominated networks characterized by complex multi-timescale dynamics and new stability interactions over a wide frequency range. Accurate analysis of these phenomena requires high-fidelity models of transmission networks and power electronic converters, which often result in large-scale differential-algebraic systems with significant computational burden. This paper provides an analytical review of model order reduction techniques for converter-rich power systems, with particular emphasis on the key equations employed in the reduction process. Advantages and limitations of commonly used strategies, including timescale-based singular perturbation, projection-based, operator-based, data-driven, and machine-learning based methods, are discussed. The synthesis highlights key challenges related to harmonic interactions and multi-frequency dynamics, and outlines directions for the development of computationally efficient yet dynamically accurate reduced-order models for future power systems.

The integration of power electronic converters (PECs) and distributed energy resources (DERs) in modern power systems has introduced dynamism and complexity. Accurate simulation becomes essential to comprehend the influence of converter domination on the power grid. This study addresses the fast-switching and stochastic behaviors exhibited by inverter-based resources in converter-dominated power systems, highlighting the necessity for precise analytical models. In the realm of modeling real-world systems, multiple methodologies exist. Notably, black-box and data-driven system identification techniques are employed to construct PEC models using experimental data, without relying on a priori knowledge of the internal system physics. This approach entails a systematic process of model class selection, parameter estimation, and model validation. While a range of linear and nonlinear model structures and estimation algorithms are at our disposal, it remains imperative to harness creativity and a profound understanding of the physical system to craft data-driven models that align seamlessly with their intended applications. These applications may encompass simulation, prediction, control, or fault detection. This report offers valuable insights into the collection of datasets from commercial off-the-shelf inverters, along with the presentation of intricate simulation models.

In this paper, we propose a probabilistic physics-guided framework, termed Physics-guided Deep Markov Model (PgDMM). The framework targets the inference of the characteristics and latent structure of nonlinear dynamical systems from measurement data, where exact inference of latent variables is typically intractable. A recently surfaced option pertains to leveraging variational inference to perform approximate inference. In such a scheme, transition and emission functions of the system are parameterized via feed-forward neural networks (deep generative models). However, due to the generalized and highly versatile formulation of neural network functions, the learned latent space often lacks physical interpretation and structured representation. To address this, we bridge physics-based state space models with Deep Markov Models, thus delivering a hybrid modeling framework for unsupervised learning and identification of nonlinear dynamical systems. The proposed framework takes advantage of the expressive power of deep learning, while retaining the driving physics of the dynamical system by imposing physics-driven restrictions on the side of the latent space. We demonstrate the benefits of such a fusion in terms of achieving improved performance on illustrative simulation examples and experimental case studies of nonlinear systems. Our results indicate that the physics-based models involved in the employed transition and emission functions essentially enforce a more structured and physically interpretable latent space, which is essential for enhancing and generalizing the predictive capabilities of deep learning-based models.

High Power Laser (HPL) systems operate in the attoseconds regime -- the shortest timescale ever created by humanity. HPL systems are instrumental in high-energy physics, leveraging ultra-short impulse durations to yield extremely high intensities, which are essential for both practical applications and theoretical advancements in light-matter interactions. Traditionally, the parameters regulating HPL optical performance have been manually tuned by human experts, or optimized using black-box methods that can be computationally demanding. Critically, black box methods rely on stationarity assumptions overlooking complex dynamics in high-energy physics and day-to-day changes in real-world experimental settings, and thus need to be often restarted. Deep Reinforcement Learning (DRL) offers a promising alternative by enabling sequential decision making in non-static settings. This work explores the feasibility of applying DRL to HPL systems, extending the current research by (1) learning a control policy relying solely on non-destructive image observations obtained from readily available diagnostic devices, and (2) retaining performance when the underlying dynamics vary. We evaluate our method across various test dynamics, and observe that DRL effectively enables cross-domain adaptability, coping with dynamics' fluctuations while achieving 90\% of the target intensity in test environments.

The second-order Kuramoto model captures rotor dynamics relevant to synchronization in power grids. In actual power grids, violation of angle-stability limits can trigger protective actions that are not included in the model, restricting its validity to trajectories that remain within these limits. We therefore define the secured basin as the region of disturbance space comprising disturbances whose trajectories remain within the angle-stability limits throughout the transient. We then characterize the secured basin through energy barriers, quantifying their characteristic energy scale and heterogeneity across perturbation directions. Across seven power-grid models, this characterization revealed angle-stability vulnerabilities overlooked when stability is assessed solely by the final synchronization state. It also showed that the two energy-barrier measures characterizing the secured basin exhibit distinct associations with structural connectivity and dynamical parameters. This characterization further offers practical advantages, as energy thresholds derived from state-space perturbations remain effective in distinguishing secured and unsecured outcomes under short-duration power disturbances and can be estimated efficiently by concentrating simulations near the secured-basin boundary. Overall, the secured-basin framework provides a useful basis for distinguishing node-level structural and dynamical influences on transient stability in oscillator networks with synchronization constraints.

Web search provides a promising way for people to obtain information and has been extensively studied. With the surgence of deep learning and large-scale pre-training techniques, various neural information retrieval models are proposed and they have demonstrated the power for improving search (especially, the ranking) quality. All these existing search methods follow a common paradigm, i.e. index-retrieve-rerank, where they first build an index of all documents based on document terms (i.e., sparse inverted index) or representation vectors (i.e., dense vector index), then retrieve and rerank retrieved documents based on similarity between the query and documents via ranking models. In this paper, we explore a new paradigm of information retrieval with neither sparse nor dense index but only a model. Specifically, we propose a pre-training model-based IR system called DynamicRetriever. As for this system, the training stage embeds the token-level and document-level information (especially, document identifiers) of the corpus into the model parameters, then the inference stage directly generates document identifiers for a given query. Compared with existing search methods, the model-based IR system has two advantages: i) it parameterizes the traditional static index with a pre-training model, which converts the document semantic mapping into a dynamic and updatable process; ii) with separate document identifiers, it captures both the term-level and document-level information for each document. Extensive experiments conducted on the public search benchmark MS MARCO verify the effectiveness and potential of our proposed new paradigm for information retrieval.

Artificial Intelligence (AI) data centers are emerging as converter-dominated, parameter-rich electrical systems whose dynamic response depends on fast workload-driven demand variations, tightly regulated data-hall converters, and coordinated on-site sources. Assessing such systems by repeatedly solving nonlinear time-domain models for every outage, load realization, and parameter perturbation is computationally expensive and provides limited insight into response sensitivity. This paper presents a trajectory sensitivity (TS)-based dynamic assessment framework for a self-contained AI data center supplied by a 2 kV DC microgrid with a grid-tied interface. The model includes time-varying data-hall load profiles, a voltage source converter (VSC), battery energy storage systems (BESS) units, supercapacitors, and synchronous-generation-side sources. For each disturbance, firstly, TS are computed along the nonlinear disturbance trajectory, capturing the local effect of source trips, data-hall outages, converter controls, and load ramps. Later, the computed TS data is used to estimate system trajectories under simultaneous parameter perturbations. Validation against full nonlinear ODE simulations with pm 15% perturbations shows close agreement. In addition, the TS-based approach reduces computational time of dynamic-response evaluations from seconds to milliseconds, demonstrating its potential as a scalable screening tool for AI data center dynamics.

Large-language-model (LLM)-based AI agents have recently showcased impressive versatility by employing dynamic reasoning, an adaptive, multi-step process that coordinates with external tools. This shift from static, single-turn inference to agentic, multi-turn workflows broadens task generalization and behavioral flexibility, but it also introduces serious concerns about system-level cost, efficiency, and sustainability. This paper presents the first comprehensive system-level analysis of AI agents, quantifying their resource usage, latency behavior, energy consumption, and datacenter-wide power consumption demands across diverse agent designs and test-time scaling strategies. We further characterize how AI agent design choices, such as few-shot prompting, reflection depth, and parallel reasoning, impact accuracy-cost tradeoffs. Our findings reveal that while agents improve accuracy with increased compute, they suffer from rapidly diminishing returns, widening latency variance, and unsustainable infrastructure costs. Through detailed evaluation of representative agents, we highlight the profound computational demands introduced by AI agent workflows, uncovering a looming sustainability crisis. These results call for a paradigm shift in agent design toward compute-efficient reasoning, balancing performance with deployability under real-world constraints.

Streaming video large language models (LLMs) are increasingly used for real-time multimodal tasks such as video captioning, question answering, conversational agents, and augmented reality. However, these models face fundamental memory and computational challenges because their key-value (KV) caches grow substantially with continuous streaming video input. This process requires an iterative prefill stage, which is a unique feature of streaming video LLMs. Due to its iterative prefill stage, it suffers from significant limitations, including extensive computation, substantial data transfer, and degradation in accuracy. Crucially, this issue is exacerbated for edge deployment, which is the primary target for these models. In this work, we propose V-Rex, the first software-hardware co-designed accelerator that comprehensively addresses both algorithmic and hardware bottlenecks in streaming video LLM inference. At its core, V-Rex introduces ReSV, a training-free dynamic KV cache retrieval algorithm. ReSV exploits temporal and spatial similarity-based token clustering to reduce excessive KV cache memory across video frames. To fully realize these algorithmic benefits, V-Rex offers a compact, low-latency hardware accelerator with a dynamic KV cache retrieval engine (DRE), featuring bit-level and early-exit based computing units. V-Rex achieves unprecedented real-time of 3.9-8.3 FPS and energy-efficient streaming video LLM inference on edge deployment with negligible accuracy loss. While DRE only accounts for 2.2% power and 2.0% area, the system delivers 1.9-19.7x speedup and 3.1-18.5x energy efficiency improvements over AGX Orin GPU. This work is the first to comprehensively tackle KV cache retrieval across algorithms and hardware, enabling real-time streaming video LLM inference on resource-constrained edge devices.

Despite recent advances in natural language understanding and generation, and decades of research on the development of conversational bots, building automated agents that can carry on rich open-ended conversations with humans "in the wild" remains a formidable challenge. In this work we develop a real-time, open-ended dialogue system that uses reinforcement learning (RL) to power a bot's conversational skill at scale. Our work pairs the succinct embedding of the conversation state generated using SOTA (supervised) language models with RL techniques that are particularly suited to a dynamic action space that changes as the conversation progresses. Trained using crowd-sourced data, our novel system is able to substantially exceeds the (strong) baseline supervised model with respect to several metrics of interest in a live experiment with real users of the Google Assistant.

The increasing capability of Large Language Models to act as human-like social agents raises two important questions in the area of opinion dynamics. First, whether these agents can generate effective arguments that could be injected into the online discourse to steer the public opinion. Second, whether artificial agents can interact with each other to reproduce dynamics of persuasion typical of human social systems, opening up opportunities for studying synthetic social systems as faithful proxies for opinion dynamics in human populations. To address these questions, we designed a synthetic persuasion dialogue scenario on the topic of climate change, where a 'convincer' agent generates a persuasive argument for a 'skeptic' agent, who subsequently assesses whether the argument changed its internal opinion state. Different types of arguments were generated to incorporate different linguistic dimensions underpinning psycho-linguistic theories of opinion change. We then asked human judges to evaluate the persuasiveness of machine-generated arguments. Arguments that included factual knowledge, markers of trust, expressions of support, and conveyed status were deemed most effective according to both humans and agents, with humans reporting a marked preference for knowledge-based arguments. Our experimental framework lays the groundwork for future in-silico studies of opinion dynamics, and our findings suggest that artificial agents have the potential of playing an important role in collective processes of opinion formation in online social media.

Price responsiveness is a major feature of end use customers (EUCs) that participate in demand response (DR) programs, and has been conventionally modeled with static demand functions, which take the electricity price as the input and the aggregate energy consumption as the output. This, however, neglects the inherent temporal correlation of the EUC behaviors, and may result in large errors when predicting the actual responses of EUCs in real-time pricing (RTP) programs. In this paper, we propose a dynamical DR model so as to capture the temporal behavior of the EUCs. The states in the proposed dynamical DR model can be explicitly chosen, in which case the model can be represented by a linear function or a multi-layer feedforward neural network, or implicitly chosen, in which case the model can be represented by a recurrent neural network or a long short-term memory unit network. In both cases, the dynamical DR model can be learned from historical price and energy consumption data. Numerical simulation illustrated how the states are chosen and also showed the proposed dynamical DR model significantly outperforms the static ones.

Evaluations of LLM planning agents largely ask whether a task succeeds or a declared plan is followed. In strategic cyber-physical systems, a stronger question is whether the planning architecture remains appropriate after autonomous participants respond and physics constrains the outcome. We introduce a controlled, physics-grounded benchmark built around planning-induced control trajectories: the ordered planning operations and directives through which an execution architecture acts on other agents and the physical process. It implements predefined, sequential, hierarchical, and search executors in a smart-grid demand-response system with 40 heterogeneous prosumers and an independently simulated radial feeder. The LLM is bounded to typed policy declaration and short operator messages, while schedule construction, prosumer dynamics, and power flow remain explicit code. The protocol uses paired forced-mode counterfactuals, common random response draws, and event-level deadline feasibility. Three properties follow. Architecture materially changes outcomes: forced search is the oracle in all five baseline seeds. Execution fidelity needs more than mode agreement: objective substitution holds agreement at 1.0 while increasing voltage shortfall by 2.68x. A 144-scenario, 576-episode bank has feasible oracles from three of the four architectures. A prespecified stress-held-out ridge has mean regret 90.7 (95% interval [73.8, 108.6]) and no detectable value over fixed sequential; applying known deadline feasibility before quality prediction cuts regret to 29.0 and improves over fixed sequential by 61.1. An all-feasible ablation does not beat fixed search, localising the remaining challenge to within-feasible quality selection. A five-model extension separates stress-conditioned, state-blind, and invariant declarers; latency tails show that live feasibility should be treated probabilistically.

Open Radio Access Network systems, with their virtualized base stations (vBSs), offer operators the benefits of increased flexibility, reduced costs, vendor diversity, and interoperability. Optimizing the allocation of resources in a vBS is challenging since it requires knowledge of the environment, (i.e., "external'' information), such as traffic demands and channel quality, which is difficult to acquire precisely over short intervals of a few seconds. To tackle this problem, we propose an online learning algorithm that balances the effective throughput and vBS energy consumption, even under unforeseeable and "challenging'' environments; for instance, non-stationary or adversarial traffic demands. We also develop a meta-learning scheme, which leverages the power of other algorithmic approaches, tailored for more "easy'' environments, and dynamically chooses the best performing one, thus enhancing the overall system's versatility and effectiveness. We prove the proposed solutions achieve sub-linear regret, providing zero average optimality gap even in challenging environments. The performance of the algorithms is evaluated with real-world data and various trace-driven evaluations, indicating savings of up to 64.5% in the power consumption of a vBS compared with state-of-the-art benchmarks.

Power flow (PF) calculations are the backbone of real-time grid operations, across workflows such as contingency analysis (where repeated PF evaluations assess grid security under outages) and topology optimization (which involves PF-based searches over combinatorially large action spaces). Running these calculations at operational timescales or across large evaluation spaces remains a major computational bottleneck. Additionally, growing uncertainty in power system operations from the integration of renewables and climate-induced extreme weather also calls for tools that can accurately and efficiently simulate a wide range of scenarios and operating conditions. Machine learning methods offer a potential speedup over traditional solvers, but their performance has not been systematically assessed on benchmarks that capture real-world variability. This paper introduces PFΔ, a benchmark dataset for power flow that captures diverse variations in load, generation, and topology. PFΔ contains 859,800 solved power flow instances spanning six different bus system sizes, capturing three types of contingency scenarios (N , N -1, and N -2), and including close-to-infeasible cases near steady-state voltage stability limits. We evaluate traditional solvers and GNN-based methods, highlighting key areas where existing approaches struggle, and identifying open problems for future research. Our dataset is available at https://huggingface.co/datasets/pfdelta/pfdelta/tree/main and our code with data generation scripts and model implementations is at https://github.com/MOSSLab-MIT/pfdelta.

Python for Power System Analysis (PyPSA) is a free software toolbox for simulating and optimising modern electrical power systems over multiple periods. PyPSA includes models for conventional generators with unit commitment, variable renewable generation, storage units, coupling to other energy sectors, and mixed alternating and direct current networks. It is designed to be easily extensible and to scale well with large networks and long time series. In this paper the basic functionality of PyPSA is described, including the formulation of the full power flow equations and the multi-period optimisation of operation and investment with linear power flow equations. PyPSA is positioned in the existing free software landscape as a bridge between traditional power flow analysis tools for steady-state analysis and full multi-period energy system models. The functionality is demonstrated on two open datasets of the transmission system in Germany (based on SciGRID) and Europe (based on GridKit).

Cascading failures in power grids can lead to grid collapse, causing severe disruptions to social operations and economic activities. In certain cases, multi-stage cascading failures can occur. However, existing cascading-failure-mitigation strategies are usually single-stage-based, overlooking the complexity of the multi-stage scenario. This paper treats the multi-stage cascading failure problem as a reinforcement learning task and develops a simulation environment. The reinforcement learning agent is then trained via the deterministic policy gradient algorithm to achieve continuous actions. Finally, the effectiveness of the proposed approach is validated on the IEEE 14-bus and IEEE 118-bus systems.

Access to realistic transmission grid models is essential for power systems research, yet detailed network data in the United States remains restricted under critical-infrastructure regulations. We present a pipeline that constructs complete, OPF-solvable transmission network models entirely from publicly available data. The five-stage pipeline (1) extracts power infrastructure from OpenStreetMap via a local Overpass API instance, (2) reconstructs bus-branch topology through voltage inference, line merging, and transformer detection, (3) estimates electrical parameters using voltage-class lookup tables calibrated with U.S. Energy Information Administration (EIA) plant-level data, (4) allocates hourly demand from EIA-930 to individual buses using US Census population as a spatial proxy, and (5) solves both DC and AC optimal power flow using PowerModels.jl with a progressive relaxation strategy that automatically loosens constraints on imprecise models. We validate the pipeline on all 48 contiguous US states and six multi-state regions, including the full Western (5,076 buses) and Eastern (21,697 buses) Interconnections. Of the 48 single-state models, 42 (88%) converge at the strictest relaxation level for AC-OPF at peak hour and 44 (92%) off-peak. Dispatch costs (median $22/MWh) and system losses (median 1.0%) are consistent with real wholesale-market outcomes. The pipeline relies exclusively on open data sources, enabling reproducible grid analysis without proprietary data. All 54 models (48 single-state and 6 multi-state) are publicly released at https://github.com/microsoft/GridSFM.

A critical aspect of power systems research is the availability of suitable data, access to which is limited by privacy concerns and the sensitive nature of energy infrastructure. This lack of data, in turn, hinders the development of modern research avenues such as machine learning approaches or stochastic formulations. To overcome this challenge, this paper proposes a systematic, data-driven framework for reconstructing high-fidelity time series, using publicly-available grid snapshots and historical data published by transmission system operators. The proposed approach, from geo-spatial data and generation capacity reconstruction, to time series disaggregation, is applied to the French transmission grid. Thereby, synthetic but highly realistic time series data, spanning multiple years with a 5-minute granularity, is generated at the individual component level.

Large language models (LLMs) have demonstrated remarkable tool-use capabilities, yet their application to power system operations remains largely unexplored. This paper presents Grid-Mind, a domain-specific LLM agent that interprets natural-language interconnection requests and autonomously orchestrates multi-fidelity power system simulations. The LLM-first architecture positions the language model as the central decision-making entity, employing an eleven-tool registry to execute Connection Impact Assessment (CIA) studies spanning steadystate power flow, N-1 contingency analysis, transient stability, and electromagnetic transient screening. A violation inspector grounds every decision in quantitative simulation outputs, while a three-layer anti-hallucination defence mitigates numerical fabrication risk through forced capacity-tool routing and post-response grounding validation. A prompt-level self-correction mechanism extracts distilled lessons from agent failures, yielding progressive accuracy improvements without model retraining. End-to-end evaluation on 50 IEEE 118-bus scenarios (DeepSeek-V3, 2026-02-23) achieved 84.0% tool-selection accuracy and 100% parsing accuracy. A separate 56-scenario self-correction suite passed 49 of 56 cases (87.5%) with a mean score of 89.3. These results establish a reproducible baseline for continued refinement while maintaining auditable, simulation-grounded decision support.

This paper proposes a cascading failure mitigation strategy based on Reinforcement Learning (RL). The motivation of the Multi-Stage Cascading Failure (MSCF) problem and its connection with the challenge of climate change are introduced. The bottom-level corrective control of the MCSF problem is formulated based on DCOPF (Direct Current Optimal Power Flow). Then, to mitigate the MSCF issue by a high-level RL-based strategy, physics-informed reward, action, and state are devised. Besides, both shallow and deep neural network architectures are tested. Experiments on the IEEE 118-bus system by the proposed mitigation strategy demonstrate a promising performance in reducing system collapses.

Electricity grid's resiliency and climate change strongly impact one another due to an array of technical and policy-related decisions that impact both. This paper introduces a physics-informed machine learning-based framework to enhance grid's resiliency. Specifically, when encountering disruptive events, this paper designs remedial control actions to prevent blackouts. The proposed Physics-Guided Reinforcement Learning (PG-RL) framework determines effective real-time remedial line-switching actions, considering their impact on power balance, system security, and grid reliability. To identify an effective blackout mitigation policy, PG-RL leverages power-flow sensitivity factors to guide the RL exploration during agent training. Comprehensive evaluations using the Grid2Op platform demonstrate that incorporating physical signals into RL significantly improves resource utilization within electric grids and achieves better blackout mitigation policies - both of which are critical in addressing climate change.

High-quality power flow datasets are essential for training machine learning models in power systems. However, security and privacy concerns restrict access to real-world data, making statistically accurate and physically consistent synthetic datasets a viable alternative. We develop a diffusion model for generating synthetic power flow datasets from real-world power grids that both replicate the statistical properties of the real-world data and ensure AC power flow feasibility. To enforce the constraints, we incorporate gradient guidance based on the power flow constraints to steer diffusion sampling toward feasible samples. For computational efficiency, we further leverage insights from the fast decoupled power flow method and propose a variable decoupling strategy for the training and sampling of the diffusion model. These solutions lead to a physics-informed diffusion model, generating power flow datasets that outperform those from the standard diffusion in terms of feasibility and statistical similarity, as shown in experiments across IEEE benchmark systems.

Flexible grid topology has become a key enabler of flexibility in modern power grids, particularly for congestion management. Studying the effects of combinatorial topological changes is therefore of significant interest, though it remains computationally intensive in most cases. To address this, we revisit the superposition theorem, which has served as the foundation for the decomposition of numerous power system problems over the past decades, particularly those involving changes in generation and loads. However, its application has traditionally been restricted to fixed grid topologies, breaking down as soon as a topology change occurs. In this paper, we extend the superposition theorem to accommodate varying grid topologies by leveraging well-known distribution factors. This unified framework applies to all types of topological changes, including line disconnection and reconnection, as well as bus splitting and merging. We provide numerical experiments to validate our approach and highlight its advantages in terms of speed-up and interpretability. Finally, we demonstrate its application in two key use cases: remedial action search and updated security analysis following a topological change. Our results show that the proposed approach achieves more than an order-of-magnitude speed-up for real-sized grids compared to the fastest power flow solvers.

Electricity systems are key to transforming today's society into a carbon-free economy. Long-term electricity market mechanisms, including auctions, support schemes, and other policy instruments, are critical in shaping the electricity generation mix. In light of the need for more advanced tools to support policymakers and other stakeholders in designing, testing, and evaluating long-term markets, this work presents a multi-agent reinforcement learning model capable of capturing the key features of decarbonizing energy systems. Profit-maximizing generation companies make investment decisions in the wholesale electricity market, responding to system needs, competitive dynamics, and policy signals. The model employs independent proximal policy optimization, which was selected for suitability to the decentralized and competitive environment. Nevertheless, given the inherent challenges of independent learning in multi-agent settings, an extensive hyperparameter search ensures that decentralized training yields market outcomes consistent with competitive behavior. The model is applied to a stylized version of the Italian electricity system and tested under varying levels of competition, market designs, and policy scenarios. Results highlight the critical role of market design for decarbonizing the electricity sector and avoiding price volatility. The proposed framework allows assessing long-term electricity markets in which multiple policy and market mechanisms interact simultaneously, with market participants responding and adapting to decarbonization pathways.

This paper revisits the concept of damping torque in a multimachine power system and its relation to the dissipation of oscillation energy in synchronous machine windings. As a multimachine extension of an existing result on a single-machine-infinite-bus (SMIB) system, we show that the total damping power for a mode stemming from the interaction of electromagnetic torques and rotor speeds is equal to the sum of average power dissipations in the generator windings corresponding to the modal oscillation. Further, counter-intuitive to the SMIB result, we demonstrate that, although the equality holds on an aggregate, such is not the case for individual machines in an interconnected system. To that end, distribution factors are derived for expressing the average damping power of each generator as a linear combination of average powers of modal energy dissipation in the windings of all machines in the system. These factors represent the distribution of damping power in a multimachine system. The results are validated on IEEE 4-machine and 16-machine test systems.

Computing is conventionally implemented by hardware engineered for information processing. Here we investigate infrastructure-native computing: the use of a physical system built for another primary function as a fixed computational operator. In time-domain simulations of an IEEE 14-bus electrical network, Kirchhoff's current law and Ohm's law relate voltage-reference perturbations applied at distributed controllable nodes interfaced by power electronics converters to current responses through a topology-dependent transformation. A trained digital encoder and decoder exploit this transformation for image classification, reaching 91.5% accuracy on MNIST and 82.25% on Fashion-MNIST. The modeled operator is represented by 933 surrogate parameters, compared with 12,340 task-trained parameters for an accuracy-matched fully connected core transformation. Current superposition further supports concurrent spatial sharing of the operator and sequential temporal reuse, with per-stream accuracies above 85% and 93%, respectively, in surrogate-model evaluations. Evaluations on CIFAR-10 and repeated 10-class tasks sampled from a Butterflies-and-Moths dataset show that the incremental utility of the physical operator depends on the representation supplied by upstream digital feature extraction. These results provide a simulation-based proof of concept for infrastructure-native computing with electrical networks and identify topology, accessible control channels, and input representation as determinants of its computational utility.

Reinforcement learning (RL) can provide adaptive and scalable controllers essential for power grid decarbonization. However, RL methods struggle with power grids' complex dynamics, long-horizon goals, and hard physical constraints. For these reasons, we present RL2Grid, a benchmark designed in collaboration with power system operators to accelerate progress in grid control and foster RL maturity. Built on RTE France's power simulation framework, RL2Grid standardizes tasks, state and action spaces, and reward structures for a systematic evaluation and comparison of RL algorithms. Moreover, we integrate operational heuristics and design safety constraints based on human expertise to ensure alignment with physical requirements. By establishing reference performance metrics for classic RL baselines on RL2Grid's tasks, we highlight the need for novel methods capable of handling real systems and discuss future directions for RL-based grid control.

Model predictive control (MPC)-based energy management systems (EMS) are essential for ensuring optimal, secure, and stable operation in microgrids with high penetrations of distributed energy resources. However, due to the high computational cost for the decision-making, the conventional MPC-based EMS typically adopts a simplified integrated-bus power balance model. While this simplification is effective for small networks, large-scale systems require a more detailed branch flow model to account for the increased impact of grid power losses and security constraints. This work proposes an efficient and reliable MPC-based EMS that incorporates power-loss effects and grid-security constraints. %, while adaptively shaping the battery power profile in response to online renewable inputs, achieving reduced operational costs. It enhances system reliability, reduces operational costs, and shows strong potential for online implementation due to its reduced computational effort. Specifically, a second-order cone program (SOCP) branch flow relaxation is integrated into the constraint set, yielding a convex formulation that guarantees globally optimal solutions with high computational efficiency. Owing to the radial topology of the microgrid, this relaxation is practically tight, ensuring equivalence to the original problem. Building on this foundation, an online demand response (DR) module is designed to further reduce the operation cost through peak shaving. To the best of our knowledge, no prior MPC-EMS framework has simultaneously modeled losses and security constraints while coordinating flexible loads within a unified architecture. The developed framework enables secure operation with effective peak shaving and reduced total cost. The effectiveness of the proposed method is validated on 10-bus, 18-bus, and 33-bus systems.

We present the PowerGridworld software package to provide users with a lightweight, modular, and customizable framework for creating power-systems-focused, multi-agent Gym environments that readily integrate with existing training frameworks for reinforcement learning (RL). Although many frameworks exist for training multi-agent RL (MARL) policies, none can rapidly prototype and develop the environments themselves, especially in the context of heterogeneous (composite, multi-device) power systems where power flow solutions are required to define grid-level variables and costs. PowerGridworld is an open-source software package that helps to fill this gap. To highlight PowerGridworld's key features, we present two case studies and demonstrate learning MARL policies using both OpenAI's multi-agent deep deterministic policy gradient (MADDPG) and RLLib's proximal policy optimization (PPO) algorithms. In both cases, at least some subset of agents incorporates elements of the power flow solution at each time step as part of their reward (negative cost) structures.

Accurate power load forecasting is essential for the efficient operation and planning of electrical grids, particularly given the increased variability and complexity introduced by renewable energy sources. This paper introduces GAT-LSTM, a hybrid model that combines Graph Attention Networks (GAT) and Long Short-Term Memory (LSTM) networks. A key innovation of the model is the incorporation of edge attributes, such as line capacities and efficiencies, into the attention mechanism, enabling it to dynamically capture spatial relationships grounded in grid-specific physical and operational constraints. Additionally, by employing an early fusion of spatial graph embeddings and temporal sequence features, the model effectively learns and predicts complex interactions between spatial dependencies and temporal patterns, providing a realistic representation of the dynamics of power grids. Experimental evaluations on the Brazilian Electricity System dataset demonstrate that the GAT-LSTM model significantly outperforms state-of-the-art models, achieving reductions of 21. 8% in MAE, 15. 9% in RMSE and 20. 2% in MAPE. These results underscore the robustness and adaptability of the GAT-LSTM model, establishing it as a powerful tool for applications in grid management and energy planning.

Dynamical systems (DS) theory is fundamental for many areas of science and engineering. It can provide deep insights into the behavior of systems evolving in time, as typically described by differential or recursive equations. A common approach to facilitate mathematical tractability and interpretability of DS models involves decomposing nonlinear DS into multiple linear DS separated by switching manifolds, i.e. piecewise linear (PWL) systems. PWL models are popular in engineering and a frequent choice in mathematics for analyzing the topological properties of DS. However, hand-crafting such models is tedious and only possible for very low-dimensional scenarios, while inferring them from data usually gives rise to unnecessarily complex representations with very many linear subregions. Here we introduce Almost-Linear Recurrent Neural Networks (AL-RNNs) which automatically and robustly produce most parsimonious PWL representations of DS from time series data, using as few PWL nonlinearities as possible. AL-RNNs can be efficiently trained with any SOTA algorithm for dynamical systems reconstruction (DSR), and naturally give rise to a symbolic encoding of the underlying DS that provably preserves important topological properties. We show that for the Lorenz and R\"ossler systems, AL-RNNs discover, in a purely data-driven way, the known topologically minimal PWL representations of the corresponding chaotic attractors. We further illustrate on two challenging empirical datasets that interpretable symbolic encodings of the dynamics can be achieved, tremendously facilitating mathematical and computational analysis of the underlying systems.

The DC Optimal Power Flow (DC-OPF) problem is fundamental to power system operations, requiring rapid solutions for real-time grid management. While traditional optimization solvers provide optimal solutions, their computational cost becomes prohibitive for large-scale systems requiring frequent recalculations. Machine learning approaches offer promise for acceleration but often struggle with constraint satisfaction and cost optimality. We present a novel two-stage learning framework that combines physics-informed Graph Neural Networks (GNNs) with Continuous Flow Matching (CFM) for solving DC-OPF problems. Our approach embeds fundamental physical principles--including economic dispatch optimality conditions, Kirchhoff's laws, and Karush-Kuhn-Tucker (KKT) complementarity conditions--directly into the training objectives. The first stage trains a GNN to produce feasible initial solutions by learning from physics-informed losses that encode power system constraints. The second stage employs CFM, a simulation-free continuous normalizing flow technique, to refine these solutions toward optimality through learned vector field regression. Evaluated on the IEEE 30-bus system across five load scenarios ranging from 70\% to 130\% nominal load, our method achieves near-optimal solutions with cost gaps below 0.1\% for nominal loads and below 3\% for extreme conditions, while maintaining 100\% feasibility. Our framework bridges the gap between fast but approximate neural network predictions and optimal but slow numerical solvers, offering a practical solution for modern power systems with high renewable penetration requiring frequent dispatch updates.

Solving the AC optimal power flow problem (AC-OPF) is critical to the efficient and safe planning and operation of power grids. Small efficiency improvements in this domain have the potential to lead to billions of dollars of cost savings, and significant reductions in emissions from fossil fuel generators. Recent work on data-driven solution methods for AC-OPF shows the potential for large speed improvements compared to traditional solvers; however, no large-scale open datasets for this problem exist. We present the largest readily-available collection of solved AC-OPF problems to date. This collection is orders of magnitude larger than existing readily-available datasets, allowing training of high-capacity data-driven models. Uniquely, it includes topological perturbations - a critical requirement for usage in realistic power grid operations. We hope this resource will spur the community to scale research to larger grid sizes with variable topology.

Power distribution networks are evolving due to the integration of DERs and increased customer participation. To maintain optimal operation, minimize losses, and meet varying load demands, frequent network reconfiguration is necessary. Traditionally, the reconfiguration task relies on optimization software and expert operators, but as systems grow more complex, faster and more adaptive solutions are required without expert intervention. Data-driven reconfiguration is gaining traction for its accuracy, speed, and robustness against incomplete network data. LLMs, with their ability to capture complex patterns, offer a promising approach for efficient and responsive network reconfiguration in evolving complex power networks. In this work, we introduce LLM4DistReconfig, a deep learning-based approach utilizing a fine-tuned LLM to solve the distribution network reconfiguration problem. By carefully crafting prompts and designing a custom loss function, we train the LLM with inputs representing network parameters such as buses, available lines, open lines, node voltages, and system loss. The model then predicts optimal reconfigurations by outputting updated network configurations that minimize system loss while meeting operational constraints. Our approach significantly reduces inference time compared to classical algorithms, allowing for near real-time optimal reconfiguration after training. Experimental results show that our method generates optimal configurations minimizing system loss for five individual and a combined test dataset. It also produces minimal invalid edges, no cycles, or subgraphs across all datasets, fulfilling domain-specific needs. Additionally, the generated responses contain less than 5% improper outputs on seen networks and satisfactory results on unseen networks, demonstrating its effectiveness and reliability for the reconfiguration task.

Power grid operation is becoming more complex due to the increase in generation of renewable energy. The recent series of Learning To Run a Power Network (L2RPN) competitions have encouraged the use of artificial agents to assist human dispatchers in operating power grids. However, the combinatorial nature of the action space poses a challenge to both conventional optimizers and learned controllers. Action space factorization, which breaks down decision-making into smaller sub-tasks, is one approach to tackle the curse of dimensionality. In this study, we propose a centrally coordinated multi-agent (CCMA) architecture for action space factorization. In this approach, regional agents propose actions and subsequently a coordinating agent selects the final action. We investigate several implementations of the CCMA architecture, and benchmark in different experimental settings against various L2RPN baseline approaches. The CCMA architecture exhibits higher sample efficiency and superior final performance than the baseline approaches. The results suggest high potential of the CCMA approach for further application in higher-dimensional L2RPN as well as real-world power grid settings.

Foundation models are transforming business workflows and boosting productivity, yet they remain largely absent from engineering domains such as power system analysis, where strict physical consistency must be enforced. We present GENCO (GEometric Neural Corrective Optimizer), a unified neural solver for steady-state transmission grid analysis that handles power flow (PF), optimal power flow (OPF), and state estimation (SE) within a single architecture and shared grid representation. To support advances in neural power system solvers, we introduce the open-source GridFM Development Framework, which standardizes synthetic data generation and training in a low-code environment. We also release large-scale datasets with millions of PF and OPF scenarios across diverse grid topologies to support reproducible benchmarking. We evaluate GENCO on the PFDelta and OPFData benchmarks against state-of-the-art neural solvers and classical solvers, including Newton-Raphson and IPOPT, as well as on real-world Hydro-Québec SCADA data. For large-scale PF, GENCO recovers the full AC operating state, including voltage magnitudes and reactive power that DC-PF cannot provide, while matching DC-PF-level active power-balance residuals. It achieves up to 30x speedups over Newton-Raphson at only 2x the runtime of DC-PF. For OPF, it achieves up to 85x speedups over IPOPT while improving feasibility, optimality, and runtime over DC-OPF. For SE, GENCO is more robust than classical weighted least squares to noisy measurements and grid parameter errors, and always returns a high-quality estimate even when weighted least squares fails to converge. Together, the unified architecture and development framework provide a new approach to large-scale steady-state grid analysis, lowering the barrier to entry for power system engineers and marking a step toward Grid Foundation Models.

Driven by advancements in sensing and computing, deep reinforcement learning (DRL)-based methods have demonstrated significant potential in effectively tackling distribution system restoration (DSR) challenges under uncertain operational scenarios. However, the data-intensive nature of DRL poses obstacles in achieving satisfactory DSR solutions for large-scale, complex distribution systems. Inspired by the transformative impact of emerging foundation models, including large language models (LLMs), across various domains, this paper explores an innovative approach harnessing LLMs' powerful computing capabilities to address scalability challenges inherent in conventional DRL methods for solving DSR. To our knowledge, this study represents the first exploration of foundation models, including LLMs, in revolutionizing conventional DRL applications in power system operations. Our contributions are twofold: 1) introducing a novel LLM-powered Physics-Informed Decision Transformer (PIDT) framework that leverages LLMs to transform conventional DRL methods for DSR operations, and 2) conducting comparative studies to assess the performance of the proposed LLM-powered PIDT framework at its initial development stage for solving DSR problems. While our primary focus in this paper is on DSR operations, the proposed PIDT framework can be generalized to optimize sequential decision-making across various power system operations.

Systemic financial risk refers to the simultaneous failure or destabilization of multiple financial institutions, often triggered by contagion mechanisms or common exposures to shocks. In this paper, we present a dynamical model of bank leverage (the ratio of asset holdings to equity) a quantity that both reflects and drives risk dynamics. We model how banks, constrained by Value-at-Risk (VaR) regulations, adjust their leverage in response to changes in the price of a single asset, assumed to be held in fixed proportion across banks. This leverage-targeting behavior introduces a procyclical feedback loop between asset prices and leverage. In the dynamics, this can manifest as logistic-like behavior with a rich bifurcation structure across model parameters. By analyzing these coupled dynamics in both isolated and interconnected bank models, we outline a framework for understanding how systemic risk can emerge from seemingly rational micro-level behavior.

Power electronic converters are becoming the main components of modern power systems due to the increasing integration of renewable energy sources. However, power converters may become unstable when interacting with the complex and time-varying power grid. In this paper, we propose an adaptive data-driven control method to stabilize power converters by using only online input-output data. Our contributions are threefold. First, we reformulate the output-feedback control problem as a state-feedback linear quadratic regulator (LQR) problem with a controllable non-minimal state, which can be constructed from past input-output signals. Second, we propose a data-enabled policy optimization (DeePO) method for this non-minimal realization to achieve efficient output-feedback adaptive control. Third, we use high-fidelity simulations to verify that the output-feedback DeePO can effectively stabilize grid-connected power converters and quickly adapt to the changes in the power grid.

Electricity price forecasting in Europe presents unique challenges due to the continent's increasingly integrated and physically interconnected power market. While recent advances in foundation models have led to substantial improvements in general time series forecasting, most existing approaches do not incorporate prior graph knowledge from the transmission topology, which can limit their ability to exploit meaningful cross-region dependencies in interconnected power systems, motivating a domain-specific foundation model. In this paper, we address this gap by first introducing a comprehensive and up-to-date dataset across 24 European countries (38 regions), spanning from 2022-01-01 to 2026-01-01. Building on this groundwork, we propose PriceFM, a probabilistic foundation model pretrained on this large dataset. Specifically, PriceFM maps each region's price and exogenous features into a comparable latent embedding via a shared Mixture-of-Experts (MoE) projection layer, then injects prior graph knowledge by constructing a sparse graph mask derived from transmission topology. Across a large-scale European benchmark, PriceFM achieves strong performance and demonstrates superior generalization under both zero-shot and full-shot evaluation compared with multiple competitive baselines.

Grid edge resources refer to distributed energy resources (DERs) located on the consumer side of the electrical grid, controlled by consumers rather than utility companies. Integrating DERs with real-time electricity pricing can better align distributed supply with system demand, improving grid efficiency and reliability. However, DER owners, known as prosumers, often lack the expertise and resources to directly participate in wholesale energy markets, limiting their ability to fully realize the economic potential of their assets. Meanwhile, as DER adoption grows, the number of prosumers participating in the energy system is expected to increase significantly, creating additional challenges in coordination and market participation. To address these challenges, we propose a mean-field game framework that enables prosumers to autonomously learn optimal decision policies based on dynamic market prices and their variable solar generation. Our framework is designed to accommodate heterogeneous agents and demonstrates the existence of a mean-field equilibrium (MFE) in a wholesale energy market with many prosumers. Additionally, we introduce an algorithm that automates prosumers' resource control, facilitating real-time decision-making for energy storage management. Numerical experiments suggest that our approach converges towards an MFE and effectively reduces peak loads and price volatility, especially during periods of external demand or supply shocks. This study highlights the potential of a fully decentralized approach to integrating DERs into wholesale markets while improving market efficiency.

Reinforcement learning (RL) is a powerful framework for optimizing decision-making in complex systems under uncertainty, an essential challenge in real-world settings, particularly in the context of the energy transition. A representative example is remote microgrids that supply power to communities disconnected from the main grid. Enabling the energy transition in such systems requires coordinated control of renewable sources like wind turbines, alongside fuel generators and batteries, to meet demand while minimizing fuel consumption and battery degradation under exogenous and intermittent load and wind conditions. These systems must often conform to extensive regulations and complex operational constraints. To ensure that RL agents respect these constraints, it is crucial to provide interpretable guarantees. In this paper, we introduce Shielded Controller Units (SCUs), a systematic and interpretable approach that leverages prior knowledge of system dynamics to ensure constraint satisfaction. Our shield synthesis methodology, designed for real-world deployment, decomposes the environment into a hierarchical structure where each SCU explicitly manages a subset of constraints. We demonstrate the effectiveness of SCUs on a remote microgrid optimization task with strict operational requirements. The RL agent, equipped with SCUs, achieves a 24% reduction in fuel consumption without increasing battery degradation, outperforming other baselines while satisfying all constraints. We hope SCUs contribute to the safe application of RL to the many decision-making challenges linked to the energy transition.

Solving the optimal power flow (OPF) problem is a fundamental task to ensure the system efficiency and reliability in real-time electricity grid operations. We develop a new topology-informed graph neural network (GNN) approach for predicting the optimal solutions of real-time ac-OPF problem. To incorporate grid topology to the NN model, the proposed GNN-for-OPF framework innovatively exploits the locality property of locational marginal prices and voltage magnitude. Furthermore, we develop a physics-aware (ac-)flow feasibility regularization approach for general OPF learning. The advantages of our proposed designs include reduced model complexity, improved generalizability and feasibility guarantees. By providing the analytical understanding on the graph subspace stability under grid topology contingency, we show the proposed GNN can quickly adapt to varying grid topology by an efficient re-training strategy. Numerical tests on various test systems of different sizes have validated the prediction accuracy, improved flow feasibility, and topology adaptivity capability of our proposed GNN-based learning framework.

Unveiling feeder topologies from data is of paramount importance to advance situational awareness and proper utilization of smart resources in power distribution grids. This tutorial summarizes, contrasts, and establishes useful links between recent works on topology identification and detection schemes that have been proposed for power distribution grids. The primary focus is to highlight methods that overcome the limited availability of measurement devices in distribution grids, while enhancing topology estimates using conservation laws of power-flow physics and structural properties of feeders. Grid data from phasor measurement units or smart meters can be collected either passively in the traditional way, or actively, upon actuating grid resources and measuring the feeder's voltage response. Analytical claims on feeder identifiability and detectability are reviewed under disparate meter placement scenarios. Such topology learning claims can be attained exactly or approximately so via algorithmic solutions with various levels of computational complexity, ranging from least-squares fits to convex optimization problems, and from polynomial-time searches over graphs to mixed-integer programs. Although the emphasis is on radial single-phase feeders, extensions to meshed and/or multiphase circuits are sometimes possible and discussed. This tutorial aspires to provide researchers and engineers with knowledge of the current state-of-the-art in tractable distribution grid learning and insights into future directions of work.

Energy markets exhibit complex causal relationships between weather patterns, generation technologies, and price formation, with regime changes occurring continuously rather than at discrete break points. Current approaches model electricity prices without explicit causal interpretation or counterfactual reasoning capabilities. We introduce Augmented Time Series Causal Models (ATSCM) for energy markets, extending counterfactual reasoning frameworks to multivariate temporal data with learned causal structure. Our approach models energy systems through interpretable factors (weather, generation mix, demand patterns), rich grid dynamics, and observable market variables. We integrate neural causal discovery to learn time-varying causal graphs without requiring ground truth DAGs. Applied to real-world electricity price data, ATSCM enables novel counterfactual queries such as "What would prices be under different renewable generation scenarios?".

As smart grids (SG) increasingly rely on advanced technologies like sensors and communication systems for efficient energy generation, distribution, and consumption, they become enticing targets for sophisticated cyberattacks. These evolving threats demand robust security measures to maintain the stability and resilience of modern energy systems. While extensive research has been conducted, a comprehensive exploration of proactive cyber defense strategies utilizing Deep Learning (DL) in {SG} remains scarce in the literature. This survey bridges this gap, studying the latest DL techniques for proactive cyber defense. The survey begins with an overview of related works and our distinct contributions, followed by an examination of SG infrastructure. Next, we classify various cyber defense techniques into reactive and proactive categories. A significant focus is placed on DL-enabled proactive defenses, where we provide a comprehensive taxonomy of DL approaches, highlighting their roles and relevance in the proactive security of SG. Subsequently, we analyze the most significant DL-based methods currently in use. Further, we explore Moving Target Defense, a proactive defense strategy, and its interactions with DL methodologies. We then provide an overview of benchmark datasets used in this domain to substantiate the discourse.{ This is followed by a critical discussion on their practical implications and broader impact on cybersecurity in Smart Grids.} The survey finally lists the challenges associated with deploying DL-based security systems within SG, followed by an outlook on future developments in this key field.

Data analytics and data science play a significant role in nowadays society. In the context of Smart Grids (SG), the collection of vast amounts of data has seen the emergence of a plethora of data analysis approaches. In this paper, we conduct a Systematic Mapping Study (SMS) aimed at getting insights about different facets of SG data analysis: application sub-domains (e.g., power load control), aspects covered (e.g., forecasting), used techniques (e.g., clustering), tool-support, research methods (e.g., experiments/simulations), replicability/reproducibility of research. The final goal is to provide a view of the current status of research. Overall, we found that each sub-domain has its peculiarities in terms of techniques, approaches and research methodologies applied. Simulations and experiments play a crucial role in many areas. The replicability of studies is limited concerning the provided implemented algorithms, and to a lower extent due to the usage of private datasets.

Hydrogen-electrical microgrids are increasingly assuming an important role on the pathway toward decarbonization of energy and transportation systems. This paper studies networked hydrogen-electrical microgrids planning (NHEMP), considering a critical but often-overlooked issue, i.e., the demand-inducing effect (DIE) associated with infrastructure development decisions. Specifically, higher refueling capacities will attract more refueling demand of hydrogen-powered vehicles (HVs). To capture such interactions between investment decisions and induced refueling demand, we introduce a decision-dependent uncertainty (DDU) set and build a trilevel stochastic-robust formulation. The upper-level determines optimal investment strategies for hydrogen-electrical microgrids, the lower-level optimizes the risk-aware operation schedules across a series of stochastic scenarios, and, for each scenario, the middle-level identifies the "worst" situation of refueling demand within an individual DDU set to ensure economic feasibility. Then, an adaptive and exact decomposition algorithm, based on Parametric Column-and-Constraint Generation (PC&CG), is customized and developed to address the computational challenge and to quantitatively analyze the impact of DIE. Case studies on an IEEE exemplary system validate the effectiveness of the proposed NHEMP model and the PC&CG algorithm. It is worth highlighting that DIE can make an important contribution to the economic benefits of NHEMP, yet its significance will gradually decrease when the main bottleneck transits to other system restrictions.

Active Voltage Control (AVC) on the Power Distribution Networks (PDNs) aims to stabilize the voltage levels to ensure efficient and reliable operation of power systems. With the increasing integration of distributed energy resources, recent efforts have explored employing multi-agent reinforcement learning (MARL) techniques to realize effective AVC. Existing methods mainly focus on the acquisition of short-term AVC strategies, i.e., only learning AVC within the short-term training trajectories of a singular diurnal cycle. However, due to the dynamic nature of load demands and renewable energy, the operation states of real-world PDNs may exhibit significant distribution shifts across varying timescales (e.g., daily and seasonal changes). This can render those short-term strategies suboptimal or even obsolete when performing continuous AVC over extended periods. In this paper, we propose a novel temporal prototype-aware learning method, abbreviated as TPA, to learn time-adaptive AVC under short-term training trajectories. At the heart of TPA are two complementary components, namely multi-scale dynamic encoder and temporal prototype-aware policy, that can be readily incorporated into various MARL methods. The former component integrates a stacked transformer network to learn underlying temporal dependencies at different timescales of the PDNs, while the latter implements a learnable prototype matching mechanism to construct a dedicated AVC policy that can dynamically adapt to the evolving operation states. Experimental results on the AVC benchmark with different PDN sizes demonstrate that the proposed TPA surpasses the state-of-the-art counterparts not only in terms of control performance but also by offering model transferability. Our code is available at https://github.com/Canyizl/TPA-for-AVC.

Complex, temporally evolving phenomena, from climate to brain activity, are governed by dynamical systems (DS). DS reconstruction (DSR) seeks to infer generative surrogate models of these from observed data, reproducing their long-term behavior. Existing DSR approaches require purpose-training for any new system observed, lacking the zero-shot and in-context inference capabilities known from LLMs. Here we introduce DynaMix, a novel multivariate ALRNN-based mixture-of-experts architecture pre-trained for DSR, the first DSR model able to generalize zero-shot to out-of-domain DS. Just from a provided context signal, without any re-training, DynaMix faithfully forecasts the long-term evolution of novel DS where existing time series (TS) foundation models, like Chronos, fail -- at a fraction of the number of parameters and orders of magnitude faster inference times. DynaMix outperforms TS foundation models in terms of long-term statistics, and often also short-term forecasts, even on real-world time series, like traffic or weather data, typically used for training and evaluating TS models, but not at all part of DynaMix' training corpus. We illustrate some of the failure modes of TS models for DSR problems, and conclude that models built on DS principles may bear a huge potential also for advancing the TS prediction field.

Causal discovery for dynamical systems poses a major challenge in fields where active interventions are infeasible. Most methods used to investigate these systems and their associated benchmarks are tailored to deterministic, low-dimensional and weakly nonlinear time-series data. To address these limitations, we present CausalDynamics, a large-scale benchmark and extensible data generation framework to advance the structural discovery of dynamical causal models. Our benchmark consists of true causal graphs derived from thousands of coupled ordinary and stochastic differential equations as well as two idealized climate models. We perform a comprehensive evaluation of state-of-the-art causal discovery algorithms for graph reconstruction on systems with noisy, confounded, and lagged dynamics. CausalDynamics consists of a plug-and-play, build-your-own coupling workflow that enables the construction of a hierarchy of physical systems. We anticipate that our framework will facilitate the development of robust causal discovery algorithms that are broadly applicable across domains while addressing their unique challenges. We provide a user-friendly implementation and documentation on https://kausable.github.io/CausalDynamics.

Executable evaluation -- checking the consequences of an agent's actions with a program rather than grading its prose -- has become a prominent way to assess tool-using AI agents in software settings. Electric power engineering has not yet had an analogous benchmark: language-model use is still dominated by retrieval and text question answering, while agents acting on power-system artifacts remain mostly academic prototypes. We introduce the Power Systems Agent Benchmark, an executable benchmark for power-engineering agents. An agent receives a structured task and returns a structured solution; a deterministic evaluator recomputes the engineering quantities, checks operational constraints, and returns a feasibility flag, a normalized score, and explicit violations. The benchmark contains 41 task families across eight areas of power engineering, from power flow and protection to stability, microgrids, reliability, power quality, and forecasting. Each task is grounded in a citable source, standard, or documented engineering formulation. To resist contamination, held-out cases are synthesized on demand by per-family generators from private seeds: the construction is inspectable, but the instances remain private. In a reference evaluation with three command-line agents, the strongest score near the compact tier's ceiling, a smaller open model trails, and public and held-out performance are broadly consistent; a separate public-split grid with OpenCode and Aider probes harness effects. The reference evaluation doubles as quality control: unanimous failures flag candidate task or evaluator defects, and it exposed a latent evaluator bug missed by self-consistency checks. The evaluators are compact deterministic surrogates, but the task contract allows their internals to be upgraded to simulator-backed checks without changing how tasks are posed or solved.

Ecological interactions are often mediated by feedbacks between organisms and their resource environments. Yet, how resource supply dynamics dictate collective dynamical phases of an ecosystem remains unclear. Here, we analyse a generalised consumer--resource model with non-reciprocal interactions to demonstrate that self-renewing versus externally-supplied resources yield fundamentally different dynamical phase diagrams. As interactions become increasingly non-reciprocal, ecosystems relying on self-renewing resources transition from stable dynamics to chaos and ultimately to infeasibility. By contrast, ecosystems with externally-supplied resources remain stable over a broader parameter range and transition to infeasibility without experiencing an intervening chaotic phase. Using the cavity method, we derive a unified stability condition applicable to a broad class of resource supply functions, explaining why externally-supplied resources can expand the stable region. We show that stability hinges crucially on the susceptibility of resources to perturbations, which depends strongly on their supply. Further, we show that external resource supply suppresses chaos in the unstable region by drastically reducing the susceptibility of resources closest to extinction. Our findings demonstrate that resource dynamics fundamentally reshape the accessible dynamical behaviours of an ecosystem, with implications for interpreting microbial community experiments.

Machine Learning (ML) techniques for Optimal Power Flow (OPF) problems have recently garnered significant attention, reflecting a broader trend of leveraging ML to approximate and/or accelerate the resolution of complex optimization problems. These developments are necessitated by the increased volatility and scale in energy production for modern and future grids. However, progress in ML for OPF is hindered by the lack of standardized datasets and evaluation metrics, from generating and solving OPF instances, to training and benchmarking machine learning models. To address this challenge, this paper introduces PGLearn, a comprehensive suite of standardized datasets and evaluation tools for ML and OPF. PGLearn provides datasets that are representative of real-life operating conditions, by explicitly capturing both global and local variability in the data generation, and by, for the first time, including time series data for several large-scale systems. In addition, it supports multiple OPF formulations, including AC, DC, and second-order cone formulations. Standardized datasets are made publicly available to democratize access to this field, reduce the burden of data generation, and enable the fair comparison of various methodologies. PGLearn also includes a robust toolkit for training, evaluating, and benchmarking machine learning models for OPF, with the goal of standardizing performance evaluation across the field. By promoting open, standardized datasets and evaluation metrics, PGLearn aims at democratizing and accelerating research and innovation in machine learning applications for optimal power flow problems. Datasets are available for download at https://www.huggingface.co/PGLearn.

Traditional frameworks of political communication operate under linear, event-driven assumptions that treat voter persuasion as a static, transactional function. This paper introduces Dynamic Consent Engineering (DCE), a novel interdisciplinary paradigm that synthesizes Edward Bernays' foundational principles of public relations with the S-E-E-D (Snowball, Equilibrium, Elasticity, Dominance) framework of system dynamics. By expanding Bernaysian operational constraints into a four-dimensional resource matrix (incorporating algorithmic media infrastructure alongside manpower, mindpower, and capital), we mathematically formalize how democratic institutions construct, optimize, and sustain political dominance. We map Bernays' classic eight-step engineering workflow directly onto non-linear feedback loops, information time lags, and demographic carrying capacities. Through rigorous modeling of systemic feedback structures, we isolate the dynamic root causes of political elasticity, policy resistance plateaus, and threshold-triggered trust collapses. Finally, we establish a four-step diagnostic pipeline and validate the framework via historical reference mode verification, demonstrating that long-term political stability depends not on ephemeral rhetoric, but on the structural synchronization of policy execution and dynamic feedback calibration.

Constrained Markov Decision Processes (CMDPs) are critical in many high-stakes applications, where decisions must optimize cumulative rewards while strictly adhering to complex nonlinear constraints. In domains such as power systems, finance, supply chains, and precision robotics, violating these constraints can result in significant financial or societal costs. Existing Reinforcement Learning (RL) methods often struggle with sample efficiency and effectiveness in finding feasible policies for highly and strictly constrained CMDPs, limiting their applicability in these environments. Stochastic dual dynamic programming is often used in practice on convex relaxations of the original problem, but they also encounter computational challenges and loss of optimality. This paper introduces a novel approach, Two-Stage Deep Decision Rules (TS-DDR), to efficiently train parametric actor policies using Lagrangian Duality. TS-DDR is a self-supervised learning algorithm that trains general decision rules (parametric policies) using stochastic gradient descent (SGD); its forward passes solve {\em deterministic} optimization problems to find feasible policies, and its backward passes leverage duality theory to train the parametric policy with closed-form gradients. TS-DDR inherits the flexibility and computational performance of deep learning methodologies to solve CMDP problems. Applied to the Long-Term Hydrothermal Dispatch (LTHD) problem using actual power system data from Bolivia, TS-DDR is shown to enhance solution quality and to reduce computation times by several orders of magnitude when compared to current state-of-the-art methods.

This study presents an integrated energy management strategy for cost optimization in multi-energy community microgrids (MGs). The proposed approach combines storage-based peak shaving, economic dispatch of diesel generators, and efficient utilization of renewable energy sources to enhance energy management in community MGs. The efficacy of the energy management system (EMS) was validated through a simulation case study for a rural Australian community. The results demonstrate that the proposed EMS effectively reduces the peak energy demand by up to 43%, lowers operational costs by 84.63% (from 189,939/year to 29,188/year), and achieves a renewable energy utilization of 92.3%, up from 47.8% in the base system. Furthermore, the levelized cost of energy was reduced by 14.21% to $0.163/kWh. The strategy ensures an uninterrupted power supply during grid outages by utilizing DGs and battery energy storage systems. The environmental benefits included a 196.4% reduction in CO2 emissions and 100% reductions in CO, unburned hydrocarbons, and particulate matter. These findings validate the feasibility of the proposed EMS in achieving cost-effective, reliable, and sustainable energy management in community MGs. These findings contribute to the field by introducing a novel approach and demonstrating the practical feasibility of multi-energy MGs.

The widespread adoption of electric vehicles (EVs) has increased the importance of demand response in smart grids. This paper proposes a two-layer demand response optimization framework for EV users and aggregators, leveraging large language models (LLMs) to balance electricity supply and demand and optimize energy utilization during EV charging. The upper-layer model, focusing on the aggregator, aims to maximize profits by adjusting retail electricity prices. The lower-layer model targets EV users, using LLMs to simulate charging demands under varying electricity prices and optimize both costs and user comfort. The study employs a multi-threaded LLM decision generator to dynamically analyze user behavior, charging preferences, and psychological factors. The framework utilizes the PSO method to optimize electricity prices, ensuring user needs are met while increasing aggregator profits. Simulation results show that the proposed model improves EV charging efficiency, alleviates peak power loads, and stabilizes smart grid operations.

Components of cyber physical systems, which affect real-world processes, are often exposed to the internet. Replacing conventional control methods with Deep Reinforcement Learning (DRL) in energy systems is an active area of research, as these systems become increasingly complex with the advent of renewable energy sources and the desire to improve their efficiency. Artificial Neural Networks (ANN) are vulnerable to specific perturbations of their inputs or features, called adversarial examples. These perturbations are difficult to detect when properly regularized, but have significant effects on the ANN's output. Because DRL uses ANN to map optimal actions to observations, they are similarly vulnerable to adversarial examples. This work proposes a novel attack technique for continuous control using Group Difference Logits loss with a bifurcation layer. By combining aspects of targeted and untargeted attacks, the attack significantly increases the impact compared to an untargeted attack, with drastically smaller distortions than an optimally targeted attack. We demonstrate the impacts of powerful gradient-based attacks in a realistic smart energy environment, show how the impacts change with different DRL agents and training procedures, and use statistical and time-series analysis to evaluate attacks' stealth. The results show that adversarial attacks can have significant impacts on DRL controllers, and constraining an attack's perturbations makes it difficult to detect. However, certain DRL architectures are far more robust, and robust training methods can further reduce the impact.

Real-world time series are often governed by complex nonlinear dynamics. Understanding these underlying dynamics is crucial for precise future prediction. While deep learning has achieved major success in time series forecasting, many existing approaches do not explicitly model the dynamics. To bridge this gap, we introduce DeepEDM, a framework that integrates nonlinear dynamical systems modeling with deep neural networks. Inspired by empirical dynamic modeling (EDM) and rooted in Takens' theorem, DeepEDM presents a novel deep model that learns a latent space from time-delayed embeddings, and employs kernel regression to approximate the underlying dynamics, while leveraging efficient implementation of softmax attention and allowing for accurate prediction of future time steps. To evaluate our method, we conduct comprehensive experiments on synthetic data of nonlinear dynamical systems as well as real-world time series across domains. Our results show that DeepEDM is robust to input noise, and outperforms state-of-the-art methods in forecasting accuracy. Our code is available at: https://abrarmajeedi.github.io/deep_edm.

Increasing levels of renewable generation motivate a growing interest in data-driven approaches for AC optimal power flow (AC OPF) to manage uncertainty; however, a lack of disciplined dataset creation and benchmarking prohibits useful comparison among approaches in the literature. To instill confidence, models must be able to reliably predict solutions across a wide range of operating conditions. This paper develops the OPF-Learn package for Julia and Python, which uses a computationally efficient approach to create representative datasets that span a wide spectrum of the AC OPF feasible region. Load profiles are uniformly sampled from a convex set that contains the AC OPF feasible set. For each infeasible point found, the convex set is reduced using infeasibility certificates, found by using properties of a relaxed formulation. The framework is shown to generate datasets that are more representative of the entire feasible space versus traditional techniques seen in the literature, improving machine learning model performance.

Autoregressive models are trained to predict a system's behavior one step at a time, and recursive generation allows the learned dynamics to unfold over long horizons. To what extent can such dynamics learned from local observations recover broader organization of an underlying system that was only partially observed during training? Here we study small autoregressive transformers trained from scratch on trajectories sampled from restricted parameter regimes of several non-linear dynamical systems, including logistic and sine maps, the Lorenz system, and the generalized Hopf system, with control parameters and state trajectories represented as sequences of continuous tokens. Under closed-loop evaluation at parameters far outside the training distribution, the models can recover self-similar period-doubling cascades, chaotic dynamics, and attractor structures with remarkable visual and numerical fidelity. For the logistic map, a transformer reproduces successive period doublings up to period 128, yielding a finite-order scaling ratio of 4.6687, matching the Feigenbaum constant to within 5times10^{-4}. We further investigate how these structures emerge over the course of training, and reveal with causal interventions how control-parameter information is processed through attention into state prediction and shapes the resulting closed-loop dynamics. These results suggest that a surprisingly narrow window into a system's local behavior may suffice for autoregressive transformers to generalize to its unseen global dynamical organization.

Dynamical systems with complex behaviours, e.g. immune system cells interacting with a pathogen, are commonly modelled by splitting the behaviour into different regimes, or modes, each with simpler dynamics, and then learning the switching behaviour from one mode to another. Switching Dynamical Systems (SDS) are a powerful tool that automatically discovers these modes and mode-switching behaviour from time series data. While effective, these methods focus on independent objects, where the modes of one object are independent of the modes of the other objects. In this paper, we focus on the more general interacting object setting for switching dynamical systems, where the per-object dynamics also depends on an unknown and dynamically changing subset of other objects and their modes. To this end, we propose a novel graph-based approach for switching dynamical systems, GRAph Switching dynamical Systems (GRASS), in which we use a dynamic graph to characterize interactions between objects and learn both intra-object and inter-object mode-switching behaviour. We introduce two new datasets for this setting, a synthesized ODE-driven particles dataset and a real-world Salsa Couple Dancing dataset. Experiments show that GRASS can consistently outperforms previous state-of-the-art methods.

Recent works exploring deep learning application to dynamical systems modeling have demonstrated that embedding physical priors into neural networks can yield more effective, physically-realistic, and data-efficient models. However, in the absence of complete prior knowledge of a dynamical system's physical characteristics, determining the optimal structure and optimization strategy for these models can be difficult. In this work, we explore methods for discovering neural state space dynamics models for system identification. Starting with a design space of block-oriented state space models and structured linear maps with strong physical priors, we encode these components into a model genome alongside network structure, penalty constraints, and optimization hyperparameters. Demonstrating the overall utility of the design space, we employ an asynchronous genetic search algorithm that alternates between model selection and optimization and obtains accurate physically consistent models of three physical systems: an aerodynamics body, a continuous stirred tank reactor, and a two tank interacting system.

Synchrophasor technology is an emerging and developing technology for monitoring and control of wide area measurement systems (WAMS). In an elementary WAMS, two identical phasors measured at two different locations have difference in the phase angles measured since their reference waveforms are not synchronized with each other. Phasor measurement units (PMUs) measure input phasors with respect to a common reference wave based on the atomic clock pulses received from global positioning system (GPS) satellites, eliminating variation in the measured phase angles due to distant locations of the measurement nodes. This has found tremendous applications in quick fault detection, fault location analysis, accurate current, voltage, frequency and phase angle measurements in WAMS. Commercially available PMU models are often proven to be expensive for research and development as well as for grid integration projects. This research article proposes an economic PMU model optimized for accurate steadystate performance based on recursive discrete Fourier transform (DFT) and provides results and detailed analysis of the proposed PMU model as per the steady state compliance specifications of IEEE standard C37.118.1. Results accurate up to 13 digits after decimal point are obtained through the developed PMU model for both nominal and off-nominal frequency inputs in steady state.

Energy system models have become indispensable tools for planning future energy systems by providing insights into different development trajectories. However, sustainable systems with high shares of renewable energy are characterized by growing cross-sectoral interdependencies and decentralized structures. To capture important properties of increasingly complex energy systems, sophisticated and flexible modelling tools are needed. At the same time, open science is becoming increasingly important in energy system modelling. This paper presents the Open Energy Modelling Framework (oemof) as a novel approach to energy system modelling, representation and analysis. The framework provides a toolbox to construct comprehensive energy system models and has been published open source under a free licence. Through collaborative development based on open processes, the framework supports a maximum level of participation, transparency and open science principles in energy system modelling. Based on a generic graph-based description of energy systems, it is well-suited to flexibly model complex cross-sectoral systems and incorporate various modelling approaches. This makes the framework a multi-purpose modelling environment for modelling and analyzing different systems at scales ranging from urban to transnational.

The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying attractor. Chaotic systems thus pose a unique challenge to modern statistical learning techniques, while retaining quantifiable mathematical properties that make them controllable and interpretable as benchmarks. Here, we present a growing database currently comprising 131 known chaotic dynamical systems spanning fields such as astrophysics, climatology, and biochemistry. Each system is paired with precomputed multivariate and univariate time series. Our dataset has comparable scale to existing static time series databases; however, our systems can be re-integrated to produce additional datasets of arbitrary length and granularity. Our dataset is annotated with known mathematical properties of each system, and we perform feature analysis to broadly categorize the diverse dynamics present across the collection. Chaotic systems inherently challenge forecasting models, and across extensive benchmarks we correlate forecasting performance with the degree of chaos present. We also exploit the unique generative properties of our dataset in several proof-of-concept experiments: surrogate transfer learning to improve time series classification, importance sampling to accelerate model training, and benchmarking symbolic regression algorithms.

State space models (SSMs) have shown remarkable empirical performance on many long sequence modeling tasks, but a theoretical understanding of these models is still lacking. In this work, we study the learning dynamics of linear SSMs to understand how covariance structure in data, latent state size, and initialization affect the evolution of parameters throughout learning with gradient descent. We show that focusing on the learning dynamics in the frequency domain affords analytical solutions under mild assumptions, and we establish a link between one-dimensional SSMs and the dynamics of deep linear feed-forward networks. Finally, we analyze how latent state over-parameterization affects convergence time and describe future work in extending our results to the study of deep SSMs with nonlinear connections. This work is a step toward a theory of learning dynamics in deep state space models.

The interaction between humans and AI in safety-critical systems presents a unique set of challenges that remain partially addressed by existing frameworks. These challenges stem from the complex interplay of requirements for transparency, trust, and explainability, coupled with the necessity for robust and safe decision-making. A framework that holistically integrates human and AI capabilities while addressing these concerns is notably required, bridging the critical gaps in designing, deploying, and maintaining safe and effective systems. This paper proposes a holistic conceptual framework for critical infrastructures by adopting an interdisciplinary approach. It integrates traditionally distinct fields such as mathematics, decision theory, computer science, philosophy, psychology, and cognitive engineering and draws on specialized engineering domains, particularly energy, mobility, and aeronautics. Its flexibility is further demonstrated through a case study on power grid management.

This paper introduces a framework specifically designed for sparse and irregular time series {risk estimation}. It is based on a Transformer Autoencoder with local attention, which leverages the powerful pattern identification capabilities of transformers complemented by traditional data cleaning and normalization methods. It efficiently captures relevant patterns within irregular sequences suffering from sparse data collection, benefiting from the discriminative ability of the local attention mechanism. The proposed framework is applied to a real-world case study, on the risk estimation of non-technical losses in electrical power systems in a wide area in Greece. Non-technical losses in electrical power systems, primarily stemming from electricity theft, pose significant economic and operational challenges. Detecting these anomalies is particularly challenging due to the inherent sparse and irregular nature of real-world data collection practices. Traditional risk estimation methods struggle with effectively capturing long-range dependencies and robustly handling such data characteristics. We demonstrate that our approach effectively yields highly discriminative latent features, which results in more consistent risk estimation compared with existing state-of-the-art and widely used methods. It achieves high recall and precision, meeting the critical objectives of the problem. As such, our solution offers a robust and effective tool for risk detection in irregular time series datasets.

Achieving robust coordination and cooperation is a central challenge in multi-agent reinforcement learning (MARL). Uncovering the mechanisms underlying such emergent behaviors calls for a dynamical understanding of learn processes. In this work, we investigate the dynamics of actor-critic agents in stochastic games, focusing on the impact of entropy regularization. By leveraging time-scale separation, we derive the system's evolution equations, which are then formally analyzed using dynamical systems theory. We find that in the constant-sum game of Matching Pennies, the system exhibits chaotic behavior. Entropy regularization mitigates this chaos and drives the dynamics toward convergence to fair cooperation. In contrast, in the general-sum game of the Prisoner's Dilemma, the system displays multistability. Interestingly, the three stable equilibria of the system correspond to the well-known ALLC (Always Cooperate), ALLD (Always Defect), and GRIM (Grim Trigger) strategies from evolutionary game theory (EGT). Entropy regularization strengthens system resilience by enlarging the basin of attraction of the cooperative equilibrium. Our findings reveal a close link between the mechanism of direct reciprocity in EGT and how cooperation emerges in MARL, offering insights for designing more robust and collaborative multi-agent systems.

This study focuses on operational control strategies for a multi-energy District Heating Network (DHN). Two control strategies are investigated and compared: (i) a reactive rule-based control (RBC) and (ii) a model predictive control (MPC). For the purpose of the study a small scale district heating network is modelled using Modelica. The production plant combines a heat pump, a gas boiler and a thermal solar field on the production side with a storage tank for flexibility purposes. On the consumption side, the virtual buildings are aggregated into a single consumer. We use our co-simulation and control platform, called Pegase, to implement the studied strategies. For both strategies the goal is to meet the consumers' demand while satisfying technical constraints. In addition MPC has the objective to minimize the operational costs, taking into account variable electricity prices and availability of solar thermal resource. Different scenarios are also defined and compared to study the effect of the heat plant sizing and forecasting error. The operational cost is reduced when switching from RBC to a MPC. As can be expected, MPC is more efficient when dealing with variable energy costs, intermittent solar energy and storage capabilities. This study also demonstrates how our tools enable an easy coupling of Modelica-based simulation with various control strategies. It especially supports the implementation and validation of complex MPC strategies in an efficient way, and yearly simulations are performed within 20 minutes.

Solving the optimal power flow (OPF) problem in real-time electricity market improves the efficiency and reliability in the integration of low-carbon energy resources into the power grids. To address the scalability and adaptivity issues of existing end-to-end OPF learning solutions, we propose a new graph neural network (GNN) framework for predicting the electricity market prices from solving OPFs. The proposed GNN-for-OPF framework innovatively exploits the locality property of prices and introduces physics-aware regularization, while attaining reduced model complexity and fast adaptivity to varying grid topology. Numerical tests have validated the learning efficiency and adaptivity improvements of our proposed method over existing approaches.

As energy systems transform to rely on renewable energy and electrification, they encounter stronger year-to-year variability in energy supply and demand. However, most infrastructure planning is based on a single weather year, resulting in a lack of robustness. In this paper, we optimize energy infrastructure for a European energy system designed for net-zero CO_2 emissions in 62 different weather years. Subsequently, we fix the capacity layouts and simulate their operation in every weather year, to evaluate resource adequacy and CO_2 emissions abatement. We show that interannual weather variability causes variation of pm10\% in total system cost. The most expensive capacity layout obtains the lowest net CO_2 emissions but not the highest resource adequacy. Instead, capacity layouts designed with years including compound weather events result in a more robust and cost-effective design. Deploying CO_2-emitting backup generation is a cost-effective robustness measure, which only increase CO_2 emissions marginally as the average CO_2 emissions remain less than 1\% of 1990 levels. Our findings highlight how extreme weather years drive investments in robustness measures, making them compatible with all weather conditions within six decades of historical weather data.

The precise knowledge regarding the state of the power grid is important in order to ensure optimal and reliable grid operation. Specifically, knowing the state of the distribution grid becomes increasingly important as more renewable energy sources are connected directly into the distribution network, increasing the fluctuations of the injected power. In this paper, we consider the case when the distribution grid becomes partially observable, and the state estimation problem is under-determined. We present a new methodology that leverages a deep neural network (DNN) to estimate the grid state. The standard DNN training method is modified to explicitly incorporate the physical information of the grid topology and line/shunt admittance. We show that our method leads to a superior accuracy of the estimation when compared to the case when no physical information is provided. Finally, we compare the performance of our method to the standard state estimation approach, which is based on the weighted least squares with pseudo-measurements, and show that our method performs significantly better with respect to the estimation accuracy.

Chaos and unpredictability are traditionally synonymous, yet large-scale machine learning methods recently have demonstrated a surprising ability to forecast chaotic systems well beyond typical predictability horizons. However, recent works disagree on whether specialized methods grounded in dynamical systems theory, such as reservoir computers or neural ordinary differential equations, outperform general-purpose large-scale learning methods such as transformers or recurrent neural networks. These prior studies perform comparisons on few individually-chosen chaotic systems, thereby precluding robust quantification of how statistical modeling choices and dynamical invariants of different chaotic systems jointly determine empirical predictability. Here, we perform the largest to-date comparative study of forecasting methods on the classical problem of forecasting chaos: we benchmark 24 state-of-the-art forecasting methods on a crowdsourced database of 135 low-dimensional systems with 17 forecast metrics. We find that large-scale, domain-agnostic forecasting methods consistently produce predictions that remain accurate up to two dozen Lyapunov times, thereby accessing a new long-horizon forecasting regime well beyond classical methods. We find that, in this regime, accuracy decorrelates with classical invariant measures of predictability like the Lyapunov exponent. However, in data-limited settings outside the long-horizon regime, we find that physics-based hybrid methods retain a comparative advantage due to their strong inductive biases.

Understanding how households consume electricity in response to socioeconomic and climatic drivers is important for decision-makers designing energy policies in a changing climate and under geopolitical tensions. Consumers respond differently to thermal stress depending on income, consumption habits and the surrounding built environment, a nonlinear behaviour that most approaches oversimplify. In this study, households are treated as agents interacting with complex environments, and Inverse Reinforcement Learning is used to represent their consumption behaviour as model implied reward functions. Specifically, we observe how these reward functions change when households undergo socioeconomic and climatic shocks. The framework is tested on different clusters of electricity consumption profiles in Italy. Clusters' reward functions are retrieved and used to understand how cooling behaviour changes from summer 2021 to summer 2022 and 2023, before, during and after the energy crisis and a heatwave. We find that these shocks reshaped cooling behaviour heterogeneously across consumer groups, in directions conditioned by their prior habits and built environment. Across the 2021 to 2023 summers, we identify a spectrum of responses: transient adjustments that receded as the shocks eased, durable shifts persisting into 2023, and consumers exhibiting negligible change. At the intradaily scale, groups comparable in socioeconomic and environmental context but differing in their daily timing of consumption responded distinctly, identifying time of use as a separate dimension of behavioural heterogeneity. Energy policies and demand-response schemes should therefore account not only for who consumers are and where they live, but for when they consume and whether their response to a shock persists.

In this study, we propose a multi branched network approach to predict the dynamics of a physics attractor characterized by intricate and chaotic behavior. We introduce a unique neural network architecture comprised of Radial Basis Function (RBF) layers combined with an attention mechanism designed to effectively capture nonlinear inter-dependencies inherent in the attractor's temporal evolution. Our results demonstrate successful prediction of the attractor's trajectory across 100 predictions made using a real-world dataset of 36,700 time-series observations encompassing approximately 28 minutes of activity. To further illustrate the performance of our proposed technique, we provide comprehensive visualizations depicting the attractor's original and predicted behaviors alongside quantitative measures comparing observed versus estimated outcomes. Overall, this work showcases the potential of advanced machine learning algorithms in elucidating hidden structures in complex physical systems while offering practical applications in various domains requiring accurate short-term forecasting capabilities.

Residential electricity demand forecasting is critical for efficient energy management and grid stability. Accurate predictions enable utility companies to optimize planning and operations. However, real-world residential electricity demand data often exhibit intricate temporal variability, including multiple seasonalities, periodicities, and abrupt fluctuations, which pose significant challenges for forecasting models. Previous models that rely on statistical methods, recurrent, convolutional neural networks, and transformers often struggle to capture these intricate temporal dynamics. To address these challenges, we propose the Seasonal-Periodic Decomposition Network (SPDNet), a novel deep learning framework consisting of two main modules. The first is the Seasonal-Trend Decomposition Module (STDM), which decomposes the input data into trend, seasonal, and residual components. The second is the Periodical Decomposition Module (PDM), which employs the Fast Fourier Transform to identify the dominant periods. For each dominant period, 1D input data is reshaped into a 2D tensor, where rows represent periods and columns correspond to frequencies. The 2D representations are then processed through three submodules: a 1D convolution to capture sharp fluctuations, a transformer-based encoder to model global patterns, and a 2D convolution to capture interactions between periods. Extensive experiments conducted on real-world residential electricity load data demonstrate that SPDNet outperforms traditional and advanced models in both forecasting accuracy and computational efficiency. The code is available in this repository: https://github.com/Tims2D/SPDNet.

We introduce controlgym, a library of thirty-six safety-critical industrial control settings, and ten infinite-dimensional partial differential equation (PDE)-based control problems. Integrated within the OpenAI Gym/Gymnasium (Gym) framework, controlgym allows direct applications of standard reinforcement learning (RL) algorithms like stable-baselines3. Our control environments complement those in Gym with continuous, unbounded action and observation spaces, motivated by real-world control applications. Moreover, the PDE control environments uniquely allow the users to extend the state dimensionality of the system to infinity while preserving the intrinsic dynamics. This feature is crucial for evaluating the scalability of RL algorithms for control. This project serves the learning for dynamics & control (L4DC) community, aiming to explore key questions: the convergence of RL algorithms in learning control policies; the stability and robustness issues of learning-based controllers; and the scalability of RL algorithms to high- and potentially infinite-dimensional systems. We open-source the controlgym project at https://github.com/xiangyuan-zhang/controlgym.

This paper presents a critical and practical approach to the evolution of distribution network reconfiguration algorithms, tracing their development from foundational heuristic methods introduced in 1975 to contemporary state-of-the-art techniques. The article systematically reviews seven different methodologies, including classical heuristic algorithms (Merlin, Baran, and others), advanced meta-heuristic methodologies (particle swarm optimization (PSO) and genetic algorithms), and purely mathematical approaches (MILP-based), analyzing their theoretical foundations, implementation strategies, computational complexity, and performance metrics based on extensive literature review and our own empirical testing. Each methodology is assessed through standardized test systems, considering multiple objectives such as power loss minimization and voltage profile improvement. The comparative analysis reveals the strengths and limitations of each approach under various network conditions and operational constraints. Furthermore, this work provides significant value to the research community by offering an open-source repository containing documented implementations of all reviewed algorithms. This resource facilitates accessibility for newcomers to the field, promotes reproducible research, and accelerates the development of next-generation distribution network optimization solutions. The repository includes comprehensive documentation, test cases, and performance benchmarks.

While the rapid expansion of data centers poses challenges for power grids, it also offers new opportunities as potentially flexible loads. Existing power system research often abstracts data centers as aggregate resources, while computer system research primarily focuses on optimizing GPU energy efficiency and largely ignores the grid impacts of optimized GPU power consumption. To bridge this gap, we develop a GPU-to-Grid framework that couples device-level GPU control with power system objectives. We study distribution-level voltage regulation enabled by flexibility in LLM inference, using batch size as a control knob that trades off the voltage impacts of GPU power consumption against inference latency and token throughput. We first formulate this problem as an optimization problem and then realize it as an online feedback optimization controller that leverages measurements from both the power grid and GPU systems. Our key insight is that reducing GPU power consumption alleviates violations of lower voltage limits, while increasing GPU power mitigates violations near upper voltage limits in distribution systems; this runs counter to the common belief that minimizing GPU power consumption is always beneficial to power grids.

As artificial intelligence models have exploded in scale and capability, understanding of their internal mechanisms remains a critical challenge. Inspired by the success of dynamical systems approaches in neuroscience, here we propose a novel framework for studying computations in deep learning systems. We focus on the residual stream (RS) in transformer models, conceptualizing it as a dynamical system evolving across layers. We find that activations of individual RS units exhibit strong continuity across layers, despite the RS being a non-privileged basis. Activations in the RS accelerate and grow denser over layers, while individual units trace unstable periodic orbits. In reduced-dimensional spaces, the RS follows a curved trajectory with attractor-like dynamics in the lower layers. These insights bridge dynamical systems theory and mechanistic interpretability, establishing a foundation for a "neuroscience of AI" that combines theoretical rigor with large-scale data analysis to advance our understanding of modern neural networks.

The undergoing energy transition is causing behavioral changes in electricity use, e.g. with self-consumption of local generation, or flexibility services for demand control. To better understand these changes and the challenges they induce, accessing individual smart meter data is crucial. Yet this is personal data under the European GDPR. A widespread use of such data requires thus to create synthetic realistic and privacy-preserving samples. This paper introduces a new synthetic load curve dataset generated by conditional latent diffusion. We also provide the contracted power, time-of-use plan and local temperature used for generation. Fidelity, utility and privacy of the dataset are thoroughly evaluated, demonstrating its good quality and thereby supporting its interest for energy modeling applications.

European countries are debating policies to mitigate the increased energy costs caused by renewed geopolitical tensions, while pursuing decarbonization and electrification. A notable example is Italy's 2026 Decreto Bollette package, which proposes to remove the carbon price equivalent from the bids of certain gas-driven power plants to wholesale electricity markets, among other provisions. We use this as a case study to assess the long-term implications of suppressing the carbon price signal in the electricity market for investment, emissions, and consumer costs. We employ a stylized Italian power system using MARLEY, a multi-agent reinforcement learning framework focused on long-term electricity market assessments. In this framework, we test this policy across configurations with varying levels of support for green investment, resource adequacy, and flexibility. Results show that partial suppression of the carbon price signal yields short-term cost reductions but only a minor long-term effect on total system costs, as the deferred emissions are ultimately repaid by consumers. CO_2 emissions rise across most configurations since suppressing the price signal erodes incentives for renewable and storage investment. Only the most ambitious configurations for supporting green investment avoid this outcome, but they do so by marginalizing the wholesale price signal itself, thereby requiring a commitment to a hybrid market paradigm that is in contradiction with the rationale of the proposed price intervention.

Deep neural networks have become increasingly of interest in dynamical system prediction, but out-of-distribution generalization and long-term stability still remains challenging. In this work, we treat the domain parameters of dynamical systems as factors of variation of the data generating process. By leveraging ideas from supervised disentanglement and causal factorization, we aim to separate the domain parameters from the dynamics in the latent space of generative models. In our experiments we model dynamics both in phase space and in video sequences and conduct rigorous OOD evaluations. Results indicate that disentangled VAEs adapt better to domain parameters spaces that were not present in the training data. At the same time, disentanglement can improve the long-term and out-of-distribution predictions of state-of-the-art models in video sequences.

Combined electric power system and High-Altitude Electromagnetic Pulse (HEMP) models are being developed to determine the effect of a HEMP on the US power grid. The work relies primarily on deterministic methods; however, it is computationally untenable to evaluate the E1 HEMP response of large numbers of grid components distributed across a large interconnection. Further, the deterministic assessment of these components' failures are largely unachievable. E1 HEMP laboratory testing of the components is accomplished, but is expensive, leaving few data points to construct failure models of grid components exposed to E1 HEMP. The use of Bayesian priors, developed using the subject matter expertise, combined with the minimal test data in a Bayesian inference process, provides the basis for the development of more robust and cost-effective statistical component failure models. These can be used with minimal computational burden in a simulation environment such as sampling of Cumulative Distribution Functions (CDFs).

AI agents are becoming increasingly capable of generating scientific code, but generating code is not the same as improving the algorithms behind it. For numerical solvers, execution feedback can expose poor performance, but rarely reveals its underlying cause and how to address it. We introduce Auto-Diagnosis and Skill Discovery (ADSD), a framework that links numerical diagnosis to reusable solver self-improvement. ADSD follows a diagnosis-first paradigm that first explains why a solver performs poorly, then uses this diagnosis to guide the discovery of appropriate numerical methods. The resulting knowledge is packaged into reusable solver skills, turning solver improvement from trial-and-error editing into a structured process of diagnosis, discovery, and implementation. Across four challenging numerical domains--power flow equation, AC optimal power flow control, stiff ordinary differential equations, and heterogeneous diffusion PDEs--ADSD consistently improves solver accuracy, robustness, and efficiency. On GOC-500 power flow, for example, ADSD reduces mean solver error by nearly 71times, with improvements further transferring to unseen grid topologies and operating regimes.

Dynamical systems provide a comprehensive way to study complex and changing behaviors across various sciences. Many modern systems are too complicated to analyze directly or we do not have access to models, driving significant interest in learning methods. Koopman operators have emerged as a dominant approach because they allow the study of nonlinear dynamics using linear techniques by solving an infinite-dimensional spectral problem. However, current algorithms face challenges such as lack of convergence, hindering practical progress. This paper addresses a fundamental open question: When can we robustly learn the spectral properties of Koopman operators from trajectory data of dynamical systems, and when can we not? Understanding these boundaries is crucial for analysis, applications, and designing algorithms. We establish a foundational approach that combines computational analysis and ergodic theory, revealing the first fundamental barriers -- universal for any algorithm -- associated with system geometry and complexity, regardless of data quality and quantity. For instance, we demonstrate well-behaved smooth dynamical systems on tori where non-trivial eigenfunctions of the Koopman operator cannot be determined by any sequence of (even randomized) algorithms, even with unlimited training data. Additionally, we identify when learning is possible and introduce optimal algorithms with verification that overcome issues in standard methods. These results pave the way for a sharp classification theory of data-driven dynamical systems based on how many limits are needed to solve a problem. These limits characterize all previous methods, presenting a unified view. Our framework systematically determines when and how Koopman spectral properties can be learned.

Reasoning system dynamics is one of the most important analytical approaches for many scientific studies. With the initial state of a system as input, the recent graph neural networks (GNNs)-based methods are capable of predicting the future state distant in time with high accuracy. Although these methods have diverse designs in modeling the coordinates and interacting forces of the system, we show that they actually share a common paradigm that learns the integration of the velocity over the interval between the initial and terminal coordinates. However, their integrand is constant w.r.t. time. Inspired by this observation, we propose a new approach to predict the integration based on several velocity estimations with Newton-Cotes formulas and prove its effectiveness theoretically. Extensive experiments on several benchmarks empirically demonstrate consistent and significant improvement compared with the state-of-the-art methods.

The integration of machine learning tools into telecom networks, has led to two prevailing paradigms, namely, language-based systems, such as Large Language Models (LLMs), and physics-based systems, such as Digital Twins (DTs). While LLM-based approaches enable flexible interaction and automation, they lack explicit representations of network dynamics. DTs, in contrast, offer a high-fidelity network simulation, but remain scenario-specific and are not designed for learning or decision-making under uncertainty. This gap becomes critical for 6G systems, where decisions must take into account the evolving network states, uncertainty, and the cascading effects of control actions across multiple layers. In this article, we introduce the {Telecom World Model}~(TWM) concept, an architecture for learned, action-conditioned, uncertainty-aware modeling of telecom system dynamics. We decompose the problem into two interacting worlds, a controllable system world consisting of operator-configurable settings and an external world that captures propagation, mobility, traffic, and failures. We propose a three-layer architecture, comprising a field world model for spatial environment prediction, a control/dynamics world model for action-conditioned Key Performance Indicator (KPI) trajectory prediction, and a telecom foundation model layer for intent translation and orchestration. We showcase a comparative analysis between existing paradigms, which demonstrates that TWM jointly provides telecom state grounding, fast action-conditioned roll-outs, calibrated uncertainty, multi-timescale dynamics, model-based planning, and LLM-integrated guardrails. Furthermore, we present a proof-of-concept on network slicing to validate the proposed architecture, showing that the full three-layer pipeline outperforms single-world baselines and accurately predicts KPI trajectories.

We put forward the dynamical study of a novel higher-order small network of Chialvo neurons arranged in a ring-star topology, with the neurons interacting via linear diffusive couplings. This model is perceived to imitate the nonlinear dynamical properties exhibited by a realistic nervous system where the neurons transfer information through higher-order multi-body interactions. We first analyze our model using the tools from nonlinear dynamics literature: fixed point analysis, Jacobian matrix, and bifurcation patterns. We observe the coexistence of chaotic attractors, and also an intriguing route to chaos starting from a fixed point, to period-doubling, to cyclic quasiperiodic closed invariant curves, to ultimately chaos. We numerically observe the existence of codimension-1 bifurcation patterns: saddle-node, period-doubling, and Neimark Sacker. We also qualitatively study the typical phase portraits of the system and numerically quantify chaos and complexity using the 0-1 test and sample entropy measure respectively. Finally, we study the collective behavior of the neurons in terms of two synchronization measures: the cross-correlation coefficient, and the Kuramoto order parameter.

Post-route power recovery changes cell choices under tightly coupled timing, electrical and physical constraints, and the value of each change depends on what it costs to repair its side effects. We propose an AI-driven framework in which a learned model drives both phases of the optimization: it ranks the powerrecovery edits to try and the repair actions that follow, while deterministic electronic design automation (EDA) analyses govern every acceptance. The framework records baseline constraint margins, identifies the damage a recovery transaction introduces in each analysis view, holds pre-existing violations at their baseline rather than working them inside the power step, and caps repair spending at a fraction of the measured saving. An ensemble of gradient-boosted models predicts power change, normalized damage reduction and constraint-regression risk from action and timing-context features available before each trial; calibrated, conservative estimates feed separate acquisition scores for recovery and repair, with a deterministic fallback when the model is uncertain. Recovery and repair remain speculative until physical implementation and fresh analysis establish baseline preservation and positive net saving. We specify the contract, the learned policy, the transactional flow and a pre-registered public evaluation protocol on open designs. Evidence from a companion study on public designs supports the contract; the learned policy is proposed, and no trained-model results or proprietary design measurements are reported.

State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the observations. This paper provides a selective review of recent advancements in deep neural network-based approaches for SSMs, and presents a unified perspective for discrete time deep state space models and continuous time ones such as latent neural Ordinary Differential and Stochastic Differential Equations. It starts with an overview of the classical maximum likelihood based approach for learning SSMs, reviews variational autoencoder as a general learning pipeline for neural network-based approaches in the presence of latent variables, and discusses in detail representative deep learning models that fall under the SSM framework. Very recent developments, where SSMs are used as standalone architectural modules for improving efficiency in sequence modeling, are also examined. Finally, examples involving mixed frequency and irregularly-spaced time series data are presented to demonstrate the advantage of SSMs in these settings.

The maritime industry's continuous commitment to sustainability has led to a dedicated exploration of methods to reduce vessel fuel consumption. This paper undertakes this challenge through a machine learning approach, leveraging a real-world dataset spanning two years of a ferry in west coast Canada. Our focus centers on the creation of a time series forecasting model given the dynamic and static states, actions, and disturbances. This model is designed to predict dynamic states based on the actions provided, subsequently serving as an evaluative tool to assess the proficiency of the ferry's operation under the captain's guidance. Additionally, it lays the foundation for future optimization algorithms, providing valuable feedback on decision-making processes. To facilitate future studies, our code is available at https://github.com/pagand/model_optimze_vessel/tree/AAAI

Standard continuous-depth models, such as Neural Ordinary Differential Equations (NODEs), offer significant advantages in modeling physical systems by learning continuous vector fields rather than discrete temporal steps. However, when applied to complex dynamical systems, standard NODEs frequently struggle with highly nonlinear dynamics. This paper investigates the Frequency-domain Neural ODE (FNODE), an architecture that projects continuous temporal dynamics into the frequency domain using the Fast Fourier Transform (FFT). By operating in the frequency domain, the model provides better generalization to the dynamical system. The architecture is empirically evaluated against discrete models, specifically Gated Recurrent Units (GRUs) and Long Short-Term Memory (LSTMs), and other continuous-depth variants, including Augmented Neural ODE (ANODE), across four distinct dynamical systems: the Lotka-Volterra model, the forced Duffing oscillator, the Van der Pol oscillator, and the Lorenz system. To rigorously assess generalization and robustness, curriculum and ensemble learning are used to evaluate the model's convergence by estimating confidence intervals across different ensemble models. The empirical results demonstrate that the FNODE architecture achieves better generalization while exhibiting remarkable convergence stability.

Common-pool resource governance requires users to cooperate and avoid overexploitation, but defection and free-riding often undermine cooperation. We model a human-environmental system that integrates dynamics of resource and users' strategies. The resource follows a logistic function that depends on natural growth rate, carrying capacity, and extraction rates of cooperators and defectors. The users' strategies evolve according to different processes that capture effects of payoff, resource, and noise. We analyze the feedback between resource availability and strategic adaptation, and explores the conditions for the emergence and maintenance of cooperation. We find different processes lead to different regimes of equilibrium solutions and resource levels depending on the parameter configuration and initial conditions. We also show that some processes can enhance the sustainability of the resource by making the users more responsive to the resource scarcity. The paper advances the understanding of human-environmental system and offers insights for resource governance policies and interventions.

Wind power is attracting increasing attention around the world due to its renewable, pollution-free, and other advantages. However, safely and stably integrating the high permeability intermittent power energy into electric power systems remains challenging. Accurate wind power forecasting (WPF) can effectively reduce power fluctuations in power system operations. Existing methods are mainly designed for short-term predictions and lack effective spatial-temporal feature augmentation. In this work, we propose a novel end-to-end wind power forecasting model named Hierarchical Spatial-Temporal Transformer Network (HSTTN) to address the long-term WPF problems. Specifically, we construct an hourglass-shaped encoder-decoder framework with skip-connections to jointly model representations aggregated in hierarchical temporal scales, which benefits long-term forecasting. Based on this framework, we capture the inter-scale long-range temporal dependencies and global spatial correlations with two parallel Transformer skeletons and strengthen the intra-scale connections with downsampling and upsampling operations. Moreover, the complementary information from spatial and temporal features is fused and propagated in each other via Contextual Fusion Blocks (CFBs) to promote the prediction further. Extensive experimental results on two large-scale real-world datasets demonstrate the superior performance of our HSTTN over existing solutions.

Magnetic field-line transport in magnetically confined plasmas is commonly modeled as diffusion through stochastic magnetic layers generated by resonant perturbations. However, experimentally relevant magnetic configurations frequently exhibit transport rates that are substantially slower than predicted by fully stochastic models, indicating the presence of unresolved dynamical barriers. In this work, we investigate the role of nested resonant island chains and their associated invariant manifolds in regulating transport within the edge magnetic topology of DIII-D tokamak discharge #171491 subjected to strong n=3 resonant magnetic perturbations. Using field-line tracing, Poincare analysis, and manifold calculations, we identify a hierarchy of homoclinic and heteroclinic tangles associated with both period-one and period-ten hyperbolic points. A systematic construction based on primary intersection points is developed to extract partial transport barriers from the full manifold geometry and divide the chaotic region into dynamically distinct domains. Monte Carlo simulations reveal that field-line escape exhibits a bi-exponential character when only the outermost period-one boundary is considered, reflecting the presence of a long-lived "sticky" region associated with the period-ten island chain. When the inner period-ten boundary is explicitly incorporated into the Monte Carlo, the escape process becomes approximately single exponential and is accurately described by turnstile lobe transport. The measured escape rate agrees with predictions obtained from the turnstile lobe area and the symplectic structure of the field-line map. These results demonstrate that nested tangles provide a quantitative transport skeleton governing magnetic-field-line escape and establish a framework for analyzing transport barriers, cantori, and lobe dynamics in realistic fusion-plasma magnetic configurations.

Dynamic Mode Decomposition (DMD) is an equation-free method that aims at reconstructing the best linear fit from temporal datasets. In this paper, we show that DMD does not provide accurate approximation for datasets describing oscillatory dynamics, like spiral waves and relaxation oscillations, or spatio-temporal Turing instability. Inspired from the classical "divide and conquer" approach, we propose a piecewise version of DMD (pDMD) to overcome this problem. The main idea is to split the original dataset in N submatrices and then apply the exact (randomized) DMD method in each subset of the obtained partition. We describe the pDMD algorithm in detail and we introduce some error indicators to evaluate its performance when N is increased. Numerical experiments show that very accurate reconstructions are obtained by pDMD for datasets arising from time snapshots of some reaction-diffusion PDE systems, like the FitzHugh-Nagumo model, the lambda-omega system and the DIB morpho-chemical system for battery modeling.

This chapter offers a principled approach to the prediction of chaotic systems from data. First, we introduce some concepts from dynamical systems' theory and chaos theory. Second, we introduce machine learning approaches for time-forecasting chaotic dynamics, such as echo state networks and long-short-term memory networks, whilst keeping a dynamical systems' perspective. Third, the lecture contains informal interpretations and pedagogical examples with prototypical chaotic systems (e.g., the Lorenz system), which elucidate the theory. The chapter is complemented by coding tutorials (online) at https://github.com/MagriLab/Tutorials.

Accurate forecasts of electricity prices are crucial for the management of electric power systems and the development of smart applications. European electricity prices have risen substantially and became highly volatile after the Russian invasion of Ukraine, challenging established forecasting methods. Here, we present a Long Short-Term Memory (LSTM) model for the German-Luxembourg day-ahead electricity prices addressing these challenges. The recurrent structure of the LSTM allows the model to adapt to trends, while the joint prediction of both mean and standard deviation enables a probabilistic prediction. Using a physics-inspired approach - superstatistics - to derive an explanation for the statistics of prices, we show that the LSTM model faithfully reproduces both prices and their volatility.

The paper sets forth comprehensive basics of Discrete Thermodynamics of Chemical Equilibria (DTD), developed by the author during the last decade and spread over series of publications. Based on the linear equations of irreversible thermodynamics, De Donder's definition of the thermodynamic force, and the Le Chatelier principle, DTD brings forward a notion of chemical equilibrium as a balance of internal and external thermodynamic forces, acting against a chemical system. The basic expression of DTD is a logistic map that ties together energetic characteristics of the chemical transformation in the system, its deviation from true thermodynamic equilibrium, and the sum of thermodynamic forces, causing that deviation. System deviation from thermodynamic equilibrium is the major variable of the theory. Solutions to the basic map define the chemical system domain of states comprising bifurcation diagrams with four areas, from true thermodynamic equilibrium to chaos, having specific distinctive meaning for chemical systems. The theory is derived from the currently recognized ideas of chemical thermodynamics and binds classical and contemporary thermodynamics of chemical equilibria into a unique concept. DTD opens new opportunities in understanding and analysis of equilibria in chemical systems. Some new results, included in the paper, have never been published before.

Physiological time series signals reflect complex, multi-scale dynamical processes of the human body. Existing modeling studies focus on static tasks such as classification, event forecasting, or short-horizon next step prediction, while long-horizon signal-level forecasting and predictive nature of physiological signals remain underexplored. We introduce NormWear-2, a world model that encodes both multivariate physiological signals and clinical intervention variables into a shared latent space and models their joint temporal evolution as a dynamical system. Our approach combines inference from prior pre-trained knowledge (intuition) with instant non-parametric latent state transition adaptation (insight), enabling coherent forecasting across multiple temporal scales, conditioned on heterogeneous clinical interventions. During the pretraining phase, we find that chaos-theoretic balancing of dynamical regime diversity yields more robust representations, with a smaller balanced corpus outperforming one twice its size and capturing bifurcation regimes. We evaluate the world model performance across diverse real-world physiological datasets spanning heterogeneous temporal resolutions and intervention regimes, covering daily life, point-of-care, and clinical settings, including fitness planning, hemodialysis, diabetes management, and surgical monitoring. These evaluation datasets comprise records from 8,026 subjects, spanning study durations from 3.2 hours for high-resolution signal data to 2.3 years for longitudinal clinical biomarker tracking. NormWear-2 achieves the best overall forecasting performance across time, frequency, and latent representation domains, with significant improvements over state-of-the-art time series foundation models, while maintaining competitive downstream representation quality, providing a step toward general-purpose world models for physiological signals.

Despite advances in learning-based methods, finding valid Lyapunov functions for nonlinear dynamical systems remains challenging. Current neural network approaches face two main issues: challenges in scalable verification and limited interpretability. To address these, we propose an end-to-end framework using transformers to construct analytical Lyapunov functions (local), which simplifies formal verification, enhances interpretability, and provides valuable insights for control engineers. Our framework consists of a transformer-based trainer that generates candidate Lyapunov functions and a falsifier that verifies candidate expressions and refines the model via risk-seeking policy gradient. Unlike Alfarano et al. (2024), which utilizes pre-training and seeks global Lyapunov functions for low-dimensional systems, our model is trained from scratch via reinforcement learning (RL) and succeeds in finding local Lyapunov functions for high-dimensional and non-polynomial systems. Given the analytical nature of the candidates, we employ efficient optimization methods for falsification during training and formal verification tools for the final verification. We demonstrate the efficiency of our approach on a range of nonlinear dynamical systems with up to ten dimensions and show that it can discover Lyapunov functions not previously identified in the control literature.