Model Card for FCD: Fourier Convolutional Decoder for Solar Data

FCD (Fourier Convolutional Decoder) is an autoencoder model designed to reconstruct solar images from compressed or transformed data, especially from data collected by space instruments like (Spectrometer/Telescope for Imaging X-rays) STIX on the Solar Orbiter.

FCD is lightweight, fast, and uses less energy than traditional methods, making it suitable for use onboard satellites or in limited computing environments.

It has been trained to handle solar X-ray data and produces clearer images with fewer artifacts compared to previous approaches.

Model Details

Model Description

Developed and shared by: Merve Selçuk-Şimşek
Funded by: Project RODEM by SNSF through FHNW
Model type: Autoencoder
License: MIT

Model Sources

Repository: GitHub
Paper: Fourier convolutional decoder: reconstructing solar flare images via deep learning
Demo: HuggingFace

Uses

The model takes 48 real numbers (of Fourier components, combined 24 real and 24 imaginary) as input at the code level, and reconstructs a 128x128 image corresponding to them.

How to Get Started with the Model

Use the code below to get started with the model.

# load TF-Keras
from tensorflow.keras.saving import load_model
# load the custom layer
from .filters import GaussianFilter

model = load_model('fcd.keras',
                    custom_objects={'GaussianFilter': GaussianFilter},
                    compile=False)

Please see fcd_demo for the full demonstration of how to use the model including

uploading input data,
loading the model,
prediction via model and
visualizing the output.

Training Details

Training Data

Training data can be generated via the code at GitHub.

Preprocessing

Both input and output data is multiplied with an alpha coefficient. For the inputs, Fourier components, it is for normalization. For the outputs, reconstructed solar flare images, it is to have a steady flux intensity range.

Training Hyperparameters

Training regime: Only FP32 precision, both for the data and the network.

Evaluation

Testing Data, Factors & Metrics

Testing Data

Testing data can be generated via the code at GitHub.

Metrics & Results

Image Quality

MS-SSIM: Up to 0.97 ± 0.02 (FCD, VIS_FWDFIT)
LPIPS: As low as 0.04 ± 0.03 (FCD)
PSNR: Up to 35.70 ± 3.97 (FCD)

Segmentation Accuracy

Dice Coefficient: Up to 0.83 ± 0.10 (FCD, VIS_FWDFIT)
Hausdorff Distance: As low as 5.08 ± 6.26 (FCD)

Metrics	FCD	VIS_FWDFIT	MEM_GE	CLEAN
MS-SSIM	0.97 ± 0.02	0.97 ± 0.03	0.89 ± 0.07	0.95 ± 0.03
LPIPS	0.04 ± 0.03	0.05 ± 0.04	0.07 ± 0.04	0.11 ± 0.04
PSNR	35.70 ± 3.97	35.50 ± 4.78	32.22 ± 3.93	31.77 ± 3.26
Dice Coefficient	0.83 ± 0.08	0.83 ± 0.10	0.76 ± 0.10	0.76 ± 0.11
Hausdorff Distance	5.08 ± 6.26	5.40 ± 7.33	34.46 ± 33.44	7.16 ± 6.56

Signal Reconstruction

MAE: As low as 0.42 ± 2.11 (MEM_GE)
Cosine Similarity: Up to 0.97 ± 0.03 (MEM_GE)
Spectral Convergence: As low as 0.27 ± 0.10 (MEM_GE)
χ²: As low as 2.14 ± 1.64 (MEM_GE)

Metrics	FCD	VIS_FWDFIT	MEM_GE	CLEAN
MAE	0.55 ± 2.78	0.59 ± 2.95	0.42 ± 2.11	0.46 ± 2.04
Cosine Similarity	0.94 ± 0.05	0.94 ± 0.06	0.97 ± 0.03	0.95 ± 0.05
Spectral Convergence	0.31 ± 0.13	0.32 ± 0.14	0.27 ± 0.10	0.32 ± 0.16
χ²	3.54 ± 5.70	3.63 ± 4.22	2.14 ± 1.64	2.98 ± 3.01

Efficiency

Time-to-Solution:
- FCD: 0.032 ± 0.005 s
- CLEAN: 0.032 ± 0.092 s
- VIS_FWDFIT: 5.522 ± 3.655 s
- MEM_GE: 9.048 ± 6.844 s

Imaging Algorithm	Time-to-Solution (s)
VIS_FWDFIT	5.522 ± 3.655
MEM_GE	9.048 ± 6.844
CLEAN	0.032 ± 0.092
FCD	0.032 ± 0.005

FCD Runtime Scaling:
- 1–10000 iterations: 0.035–2.069 s

FCD Runtime	Time-to-Solution (s)
Runtime-1	0.035 ± 0.006
Runtime-10	0.036 ± 0.010
Runtime-100	0.051 ± 0.008
Runtime-1000	0.240 ± 0.010
Runtime-10000	2.069 ± 0.039

Summary

Environmental Impact

Carbon emission is estimated using the Machine Learning Impact calculator presented in Lacoste et al. (2019).

Carbon Emitted: 0.15 kg CO2eq.
Hardware Type: 1 NVIDIA RTX A4500 GPU
Hours used: 2.5 hours
Training Type: Standard training

Technical Specifications

Model Architecture and Objective

Overcomplete Autoencoder trained in a supervised manner to reconstruct solar flare images from the Fourier components.

Compute Infrastructure

Private cluster

Hardware

NVIDIA RTX A4500 GPU

Software

Only TF-Keras (v. 2.15.0) is sufficient to run the model.

Citation

Selcuk-Simsek, M., Massa, P., Xiao, H. et al. Fourier convolutional decoder: reconstructing solar flare images via deep learning. Neural Comput & Applic (2025). https://doi.org/10.1007/s00521-025-11283-6

Model Card Contact

[email protected]

mervess
/

FCD-Solar