Application of physics-informed neural networks to modeling discontinuities in hydrodynamics and MHD*

Simulating discontinuities in magnetohydrodynamics and fluid physics has long been challenging, particularly in phenomena with shock waves that exhibit strong nonlinearities. Previous simulations of the magnetized Noh test problem1 have frequently exhibited grid-induced errors. In comparison to traditional numerical methods, the recently developed physics-informed neural networks (PINNs) are mesh-free and thus can potentially handle such irregular and moving-domain problems. In this study, we perform simulations using the PINNs algorithm for suite of standard exact solutions for problems consisting of a strong shock forming as a compressible gas moves at a constant velocity towards a rigid wall both in the presence and absence of a magnetic field. These problems include the classic the classic Sod shock problem, Noh problem, the magnetized Noh test problem. Comparison to direct numerical simulations to results from the Arbitrary Lagrangian-Eulerian Finite Volume magnetohydrodynamic code MACH2 and significance for Z-pinch simulations with a moving mesh will also be discussed.

1. Velikovich et. al., Phys. Plasmas 19, 012707 (2012).