RTMAG

In this study, we develop a physics-informed neural operator (PINO) model that learns the solution operator from 2D photospheric vector magnetic fields to 3D nonlinear force-free fields (NLFFFs). We train our PINO model using physics loss from NLFFF partial differential equations, as well as data loss from target NLFFFs. We validate our method using an analytical NLFFF model. We then train and evaluate our PINO model with 2327 numerical NLFFFs of 211 active regions from the Institute for Space-Earth Environmental Research database. The results show that our trained PINO model can generate an NLFFF within 1 s for any active region on a single consumer GPU, making real-time extrapolation of NLFFFs possible. Our artificial intelligence (AI)-generated NLFFFs are qualitatively and quantitatively quite similar to the target NLFFFs for 30 active regions. The magnetic energy of the AI-generated NLFFFs of active region 11158 follows a similar trend to the target NLFFFs as well as other conventional methods.

Example

Caution: The reliability of AI-generated NLFFFs should be further investigated in future studies.

Environment

• Python 3.11
• PyTorch
• Neural Operator

conda env create -f environment.yml
conda activate rtmag
pip install "neuraloperator<1.0"
pip install -r https://raw.githubusercontent.com/NeuralOperator/neuraloperator/main/requirements.txt
pip install -e .

Data

Low Lou (1990) NLFFF

python scripts/dataset_lowlou.py --test_path <test-path> --train_path <train-path>

After running the above command, manually select and move 5000 files for training set and 1000 files for test set.

lowlou
├── test
│   └── case1.npz
├── train_5000
│   ├── b_0.150_0.014.npz
│   ├── b_0.150_0.041.npz
│   └── ...
└── val_1000
    ├── b_0.150_0.081.npz
    ├── b_0.150_0.343.npz
    └── ...

ISEE NLFFF database

Download ISEE NLFFF and put the files in the following directory structure.

isee_data
├── 11078
│   └── 11078_20100609_000000.nc
├── 11089
│   └── 11089_20100725_000000.nc
│   ...
└── 12975
    ├── 12975NRT_20220327_120000.nc
    ├── 12975NRT_20220327_130000.nc
    └── ...

python scripts/dataset_isee.py --data_path <data-path> --dataset_path <dataset-path>

After running the above command, the files will be saved in the following directory structure.

isee_dataset
├── 11078
│   ├── input
│   │   └── input_11078_20100609_000000.npz
│   └── label
│       └── label_11078_20100609_000000.npz
├── 11089
│   ├── input
│   │   └── input_11089_20100725_000000.npz
│   └── label
│       └── label_11089_20100725_000000.npz
|   ...
└── 12975
    ├── input
    │   ├── input_12975NRT_20220327_120000.npz
    │   ├── input_12975NRT_20220327_130000.npz
    │   └── ...
    └── label
        ├── label_12975NRT_20220327_120000.npz
        ├── label_12975NRT_20220327_130000.npz
        └── ...

Train

Low Lou (1990) NLFFF

python train.py --config config/train_lowlou.json

ISEE NLFFF

python train.py --config config/train.json

Logs

tensorboard --logdir=<base_path>

Acknowledgements

• I heavily referenced the NF2 code for various tasks, such as the calculation of Low and Lou fields, metrics, and NLFFFs from PINNs. Thanks to the authors.
• I use data and code from the ISEE NLFFF database to create NLFFF datasets for real solar active regions. Thanks to the authors.
• I use streamtracer and refer to the code from flhtools for field line tracing and plotting. Thanks to the authors.
• I use pyvista for 3D field line visualization in Colab notebook. Thanks to the authors.
• I appreciate the community efforts in creating other open-source packages used in this research, such as SunPy and Astropy.

Citation

@article{Jeon_2025,
doi = {10.3847/1538-4365/adbaea},
url = {https://dx.doi.org/10.3847/1538-4365/adbaea},
year = {2025},
month = {apr},
publisher = {The American Astronomical Society},
volume = {277},
number = {2},
pages = {54},
author = {Jeon, Mingyu and Jeong, Hyun-Jin and Moon, Yong-Jae and Kang, Jihye and Kusano, Kanya},
}