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--- |
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datasets: polymathic-ai/acoustic_scattering_maze |
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tags: |
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- physics |
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--- |
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# Benchmarking Models on the Well |
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[The Well](https://github.com/PolymathicAI/the_well) is a 15TB dataset collection of physics simulations. This model is part of the models that have been benchmarked on the Well. |
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The models have been trained for a fixed time of 12 hours or up to 500 epochs, whichever happens first. The training was performed on a NVIDIA H100 96GB GPU. |
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In the time dimension, the context length was set to 4. The batch size was set to maximize the memory usage. We experiment with 5 different learning rates for each model on each dataset. |
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We use the model performing best on the validation set to report test set results. |
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The reported results are here to provide a simple baseline. **They should not be considered as state-of-the-art**. We hope that the community will build upon these results to develop better architectures for PDE surrogate modeling. |
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# Tensorized Fourier Neural Operator |
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Implementation of the [Tensorized Fourier Neural Operator](https://arxiv.org/abs/2310.00120) provided by [`neuraloperator v0.3.0`](https://neuraloperator.github.io/dev/index.html). |
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## Model Details |
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For benchmarking on the Well, we used the following parameters. |
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| Parameters | Values | |
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|------------|--------| |
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| Modes | 16 | |
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| Blocks | 4 | |
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| Hidden Size| 128 | |
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## Trained Model Versions |
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Below is the list of checkpoints available for the training of TFNO on different datasets of the Well. |
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| Dataset | Learning Rate | Epoch | VRMSE | |
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|---------|----------------|-------|-------| |
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| [acoustic_scattering_maze](https://huggingface.co/polymathic-ai/TFNO-acoustic_scattering) | 1E-3 | 27 | 0.5034 | |
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| [active_matter](https://huggingface.co/polymathic-ai/TFNO-active_matter) | 1E-3 | 243 | 0.3342 | |
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| [convective_envelope_rsg](https://huggingface.co/polymathic-ai/TFNO-convective_envelope_rsg) | 1E-3 | 13 | 0.0195 | |
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| [gray_scott_reaction_diffusion](https://huggingface.co/polymathic-ai/TFNO-gray_scott_reaction_diffusion) | 5E-3 | 45 | 0.1784 | |
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| [helmholtz_staircase](https://huggingface.co/polymathic-ai/TFNO-helmholtz_staircase) | 5E-4 | 131 | 0.00031 | |
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| [MHD_64](https://huggingface.co/polymathic-ai/TFNO-MHD_64) | 1E-3 | 155 | 0.3347 | |
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| [planetswe](https://huggingface.co/polymathic-ai/TFNO-planetswe) | 5E-4 | 49 | 0.1061 | |
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| [post_neutron_star_merger](https://huggingface.co/polymathic-ai/TFNO-post_neutron_star_merger) | 5E-4 | 99 | 0.4064 | |
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| [rayleigh_benard](https://huggingface.co/polymathic-ai/TFNO-rayleigh_benard) | 1E-4 | 31 | 0.8568 | |
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| [rayleigh_taylor_instability](https://huggingface.co/polymathic-ai/TFNO-rayleigh_taylor_instability) | 1E-4 | 175 | 0.2251 | |
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| [shear_flow](https://huggingface.co/polymathic-ai/TFNO-shear_flow) | 1E-3 | 24 | 0.3626 | |
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| [supernova_explosion_64](https://huggingface.co/polymathic-ai/TFNO-supernova_explosion_64) | 1E-4 | 35 | 0.3645 | |
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| [turbulence_gravity_cooling](https://huggingface.co/polymathic-ai/TFNO-turbulence_gravity_cooling) | 5E-4 | 10 | 0.2789 | |
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| [turbulent_radiative_layer_2D](https://huggingface.co/polymathic-ai/TFNO-turbulent_radiative_layer_2D) | 1E-3 | 500 | 0.4938 | |
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| [viscoelastic_instability](https://huggingface.co/polymathic-ai/TFNO-viscoelastic_instability) | 5E-3 | 199 | 0.7021 | |
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## Loading the model from Hugging Face |
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To load the TFNO model trained on the `acoustic_scattering_maze` of the Well, use the following commands. |
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```python |
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from the_well.benchmark.models import TFNO |
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model = TFNO.from_pretrained("polymathic-ai/TFNO-acoustic_scattering_maze") |
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``` |
