Physics-informed Attention-enhanced Fourier Neural Operator for Solar Magnetic Field Extrapolations
This work addresses solar magnetic field extrapolation for solar physics researchers, offering an incremental improvement by integrating attention mechanisms and physics-informed losses into existing neural operator frameworks.
The authors tackled the Nonlinear Force-Free Field problem in solar physics by proposing PIANO, a neural operator that learns 3D magnetic fields from 2D boundary conditions, achieving higher accuracy than state-of-the-art methods on the ISEE NLFFF dataset.
We propose Physics-informed Attention-enhanced Fourier Neural Operator (PIANO) to solve the Nonlinear Force-Free Field (NLFFF) problem in solar physics. Unlike conventional approaches that rely on iterative numerical methods, our proposed PIANO directly learns the 3D magnetic field structure from 2D boundary conditions. Specifically, PIANO integrates Efficient Channel Attention (ECA) mechanisms with Dilated Convolutions (DC), which enhances the model's ability to capture multimodal input by prioritizing critical channels relevant to the magnetic field's variations. Furthermore, we apply physics-informed loss by enforcing the force-free and divergence-free conditions in the training process so that our prediction is consistent with underlying physics with high accuracy. Experimental results on the ISEE NLFFF dataset show that our PIANO not only outperforms state-of-the-art neural operators in terms of accuracy but also shows strong consistency with the physical characteristics of NLFFF data across magnetic fields reconstructed from various solar active regions. The GitHub of this project is available https://github.com/Autumnstar-cjh/PIANO