Reconstructing Relativistic Magnetohydrodynamics with Physics-Informed Neural Networks

TL;DR

This paper develops physics-informed neural network surrogates for relativistic magnetohydrodynamics, enabling accurate, data-efficient modeling of complex plasma dynamics by directly incorporating PDE characteristics and divergence-free conditions.

Contribution

It introduces the first PINN framework for RMHD that works with primitive variables and divergence constraints, improving extrapolation and PDE violation reduction.

Findings

PINN surrogates can extrapolate RMHD dynamics in 1D and 2D.

Posterior residual-guided networks reduce PDE violations.

The MUON optimizer enhances training efficiency.

Abstract

We construct the first physics-informed neural-network (PINN) surrogates for relativistic magnetohydrodynamics (RMHD) using a hybrid PDE and data-driven workflow. Instead of training for the conservative form of the equations, we work with Jacobians or PDE characteristics directly in terms of primitive variables. We further add to the trainable system the divergence-free condition, without the need of cleaning modes. Using a novel MUON optimizer implementation, we show that a baseline PINN trained on early-time snapshots can extrapolate RMHD dynamics in one and two spatial dimensions, and that posterior residual-guided networks can systematically reduce PDE violations.