Solar Stokes Forward Modeling: Machine Learning Methods Analysis

This project implements and compares several Machine Learning and Deep Learning architectures for Forward Modeling in solar physics.
The goal is to emulate the radiative transfer equation by predicting the Stokes profiles ($I, Q, U, V$) from atmospheric physical parameters (Temperature, Magnetic Field Strength, Inclination, Azimuth).

The project benchmarks several state-of-the-art regression methods (XGBoost, PCA/F-PCA) and reproduces the study by Carroll et al. (2008), which proposed a fast method for Stokes profile synthesis, comparing them against our newly developed Deep Learning approach based on a Multi-ResNet architecture with adaptive physics-based normalization.

Citation

@article{Carroll_2008,
   title={A fast method for Stokes profile synthesis: Radiative transfer modeling for ZDI and Stokes profile inversion},
   volume={488},
   ISSN={1432-0746},
   url={http://dx.doi.org/10.1051/0004-6361:200809981},
   DOI={10.1051/0004-6361:200809981},
   number={2},
   journal={Astronomy & Astrophysics},
   publisher={EDP Sciences},
   author={Carroll, T. A. and Kopf, M. and Strassmeier, K. G.},
   year={2008},
   month={jul},
   pages={781–793}
}

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Project Structure

solar_project/
├── config/               
│   └── experiments/
│       ├── multi_resnet.yaml   
│       ├── fpca_xgboost.yaml    
│       ├── xgboost_full.yaml    
│       └── paper2008_mlp.yaml   
│
├── data/                    
│   └── atmoFe.npz         
│
├── results/                 
│
├── src/                     
│   ├── data/                
│   ├── features/            
│   ├── models/              
│   │   ├── components/      
│   │   └── wrappers.py      
│   └── model_builder.py     
│
├── run_experiment.py        
├── summary_results.py      
├── visualize_results.py     
└── requirements.txt   

Quick Start

1. Installation

Create a Python environment and install dependencies:

pip install -r requirements.txt

1. Dataset Preparation

Ensure the dataset file is placed correctly:

• Path: data/atmoFe.npz

3. Run an Experiment

To launch model training using a chosen configuration:

python run_experiment.py --config config/experiments/resnet_sobolev.yaml

After execution, the script automatically saves:

• metrics.csv: RMSE, CCC, Peak Error, Derivative Correlation
• performance.csv: training/inference timings
• model.pkl: trained model Inside:

results/<experiment_name>/

4. Compare Results

Generate a comparative table (with color highlighting) of all experiments:

python summary_results.py

5. Visualize Stokes Profiles

To generate plots comparing real vs predicted profiles:

python visualize_results.py --config config/experiments/multi_resnet.yaml --indices 0 42 100 150

This generates the file:

reconstruction_examples.png

inside the corresponding experiment results directory.

Evaluation Metrics

The project evaluates models using both statistical and physics-informed metrics to ensure that the predicted Stokes profiles are not only numerically accurate but also physically meaningful.

RMSE — Root Mean Squared Error

Measures the average squared difference between predicted and true Stokes profiles.
Useful for general regression quality.

CCC — Concordance Correlation Coefficient

Quantifies how well predictions match the ideal relation ( y = x ).
Penalizes both bias and scale mismatch, making it more informative than simple correlation.

Peak Error (%)

Measures the relative error on the maximum amplitude of each Stokes profile.
This is critical for solar physics because the amplitude of polarized lines correlates strongly with the magnetic field strength.

Derivative Correlation

Computes the correlation between the first derivatives of the predicted and true profiles.
This captures the shape, lobe structure, and asymmetries, independent of absolute intensity.

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Results

Below are the main evaluation tables for all experiments executed.
Bold entries represent the best performance per column.

RMSE

Experiment	I	Q	U	V	MEAN
pca_xgboost	0.0102	0.00614	0.00605	0.00768	0.00752
fpca_xgboost	0.01029	0.00649	0.00613	0.00769	0.00765
paper2008	0.01059	0.00402	0.00407	0.0073	0.0065
resnet_sobolev	0.00091	0.0006	0.00061	0.00074	0.00072
xgboost_full	0.00334	0.00751	0.00745	0.00707	0.00634

CCC

Experiment	I	Q	U	V	MEAN
pca_xgboost	0.99462	0.44864	0.43267	0.82144	0.67434
fpca_xgboost	0.9946	0.4488	0.43361	0.82112	0.67453
paper2008	0.99451	0.45219	0.4373	0.82153	0.67638
resnet_sobolev	0.99607	0.46201	0.44694	0.8293	0.68358
xgboost_full	0.99589	0.44569	0.42913	0.82348	0.67355

Peak Error (%)

Experiment	I	Q	U	V	MEAN
pca_xgboost	0.21429	14.5506	14.9046	4.87502	8.63614
fpca_xgboost	0.22999	16.0883	15.8843	5.09964	9.32558
paper2008	0.23285	10.7106	11.2383	5.61253	6.94858
resnet_sobolev	0.01627	2.52634	2.8788	0.87096	1.57309
xgboost_full	0.00369	19.299	19.408	6.9108	11.4054

Derivative Correlation

Experiment	I	Q	U	V	MEAN
pca_xgboost	0.97791	0.68952	0.67731	0.87014	0.80372
fpca_xgboost	0.97758	0.68766	0.67043	0.86782	0.80087
paper2008	0.97738	0.71738	0.70438	0.87002	0.81729
resnet_sobolev	0.99997	0.80298	0.79482	0.90975	0.87688
xgboost_full	0.99952	0.72421	0.71366	0.9045	0.83547

Performance

Experiment	train_time_s	throughput_ms	latency_ms
pca_xgboost	19.3983	0.07033	1303.35
fpca_xgboost	18.3872	0.01924	112.473
paper2008	259.768	0.00638	0.42656
resnet_sobolev	4158.56	0.02435	9.92212
xgboost_full	105.574	0.33767	7361.5

• throughput_ms
  This is the average time (in milliseconds) required for the model to predict one sample when processing the entire test set as a batch.
  It is computed as: throughput_ms = (total_prediction_time / number_of_samples) * 1000
• latency_ms This is the time needed to predict a single sample, measured by repeatedly calling the model on just one input: latency_ms = (time_for_50_single_predictions / 50) * 1000

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