Spectral Learning of Magnetized Plasma Dynamics: A Neural Operator Application

TL;DR

This paper demonstrates that Fourier neural operators can effectively learn and predict magnetized plasma dynamics in 2D MHD turbulence, achieving high accuracy and significant speed-ups over traditional solvers.

Contribution

The study introduces a Fourier neural operator surrogate for 2D MHD turbulence, showing superior accuracy and efficiency compared to baseline models and finite-volume solvers.

Findings

Achieves ~0.006 MSE in velocity predictions

Reproduces energy spectra within 96% accuracy

Provides 25x faster inference than finite-volume methods

Abstract

Fourier neural operators (FNOs) provide a mesh-independent way to learn solution operators for partial differential equations, yet their efficacy for magnetized turbulence is largely unexplored. Here we train an FNO surrogate for the 2-D Orszag-Tang vortex, a canonical non-ideal magnetohydrodynamic (MHD) benchmark, across an ensemble of viscosities and magnetic diffusivities. On unseen parameter settings the model achieves a mean-squared error of $\approx 6 \times 10^{-3}$ in velocity and $\approx 10^{-3}$ in magnetic field, reproduces energy spectra and dissipation rates within $96\%$ accuracy, and retains temporal coherence over long timescales. Spectral analysis shows accurate recovery of large- and intermediate-scale structures, with degradation at the smallest resolved scales due to Fourier-mode truncation. Relative to a UNet baseline the FNO cuts error by $97\%$, and compared with a high-order finite-volume solver it delivers a $25\times$ inference speed-up, offering a practical path to rapid parameter sweeps in MHD simulations.