Physics Informed Neural Networks for Magnetohydrodynamic Equations

Eva Jaillon, Pavlos Protopapas

Keywords: Physics-Informed Neural Networks, Magnetohydrodynamics, Transfer Learning, Stepwise Initialized Physics Network, High-dimensional systems

Abstract:

We present a data-free Physics-Informed Neural Network (PINN) framework for solving a coupled system of magnetohydrodynamic (MHD) equations.
Rather than introducing a new network architecture, this work focuses on a practical training strategy that enables stable optimization of large, strongly coupled PINN systems using only physical residuals. The proposed approach employs a stepwise initialization protocol, in which subsets of equations and output variables are progressively introduced while reusing previously trained weights.
This structure naturally supports transfer learning across different initial conditions and optimization regimes.
We demonstrate that the resulting model can solve the full eight-equation MHD system without observational data and can be efficiently adapted to new initial conditions using multi-head transfer learning and hybrid Adam/L-BFGS optimization, achieving substantial reductions in training time while preserving solution accuracy.

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Submission Number: 120