PHASE: Multi-Regime Modeling of Incompressible Magnetohydrodynamics

2026-09-29

AI Summary

This study addresses the high computational cost of multi-scale magnetohydrodynamic (MHD) simulations and the limited generalizability of existing models that require separate training for specific physical mechanisms. To overcome these challenges, we propose a cross-parameter adaptive neural operator framework that integrates transfer learning, mechanism-aware adaptation, physics-centric learning, and residual correction to enable efficient prediction of incompressible MHD dynamics within a single unified model. Experimental results demonstrate that this framework reduces relative errors by an order of magnitude and generalizes to unseen parameter spaces without retraining. Furthermore, it accurately captures complex physical phenomena such as Kelvin–Helmholtz instabilities, significantly enhancing both the fidelity and versatility of data-driven MHD modeling.

Abstract

Magnetohydrodynamics (MHD) is central to plasma modeling in astrophysics, space science, fusion, and engineering, but resolving multiscale MHD dynamics is computationally expensive. Machine-learning surrogates enable fast inference by learning reusable solution operators, yet existing models require separate training for each physical regime, limiting generalization across varying parameter settings. We introduce PHASE, a PHysics-Adaptive Scalable operator with residual Error correction, designed to model incompressible MHD across varying physical parameters with a single model. PHASE combines transfer learning, regime-aware adaptation, physics-centered learning, and residual refinement to improve both physical fidelity and generalization across MHD regimes. Together, these improvements achieve state-of-the-art prediction accuracy on two-dimensional MHD turbulence by reducing relative $L_2$ errors on physical fields by more than an order of magnitude compared to prior MHD neural-operator baselines. Moreover, PHASE generalizes successfully to unseen parameter values without retraining, demonstrating the cross-regime adaptability expected from operator learning. We evaluate PHASE beyond point-wise prediction errors using derived physical fields, spectral analysis, and distribution statistics, consistently observing improved physical fidelity. We further show that our framework can accurately simulate MHD instabilities by testing it on the Kelvin--Helmholtz instability, demonstrating the robustness of our method.

Problem

• Magnetohydrodynamics
• multi-regime modeling
• operator learning
• generalization
• multiscale dynamics

Innovation

• Magnetohydrodynamics
• Neural Operator
• Transfer Learning
• Residual Error Correction
• Cross-Regime Generalization