Modeling Shock-Driven MHD Turbulence with Physics-Informed Neural Networks: A Study of the Orszag-Tang Vortex

The Orszag-Tang vortex is a widely used benchmark for investigating nonlinear dynamics and the transition to supersonic 2D magnetohydrodynamic (MHD) turbulence. In this work, we employ Physics-Informed Neural Networks (PINNs) to solve the time-dependent MHD equations. By incorporating the governing physical laws, including the continuity, momentum, pressure, and induction equations, into the neural network loss function, the model learns the full spatiotemporal solution without requiring labeled training data. Numerical experiments demonstrate that PINNs can accurately capture the evolution of MHD solutions in smooth regions, but face challenges in accurately resolving discontinuous features. To address this limitation, we incorporate gradient-enhanced PINNs (gPINNs), which augment the loss function with gradient information from the governing equations. This enhancement improves accuracy in regions with steep gradients. This study highlights both the potential and limitations of PINNs-based solvers in modeling complex, nonlinear plasma dynamics and points toward the future directions for advancing their capability in resolving sharp features inherent in MHD turbulence.