Fundamental study on magnetohydrodynamic simulation method using deep learning

抄録

Some deep learning-based methods, Deep Galerkin Method (DGM), Physics Informed Neural Networks (PINNs), and others, have been suggested for solving partial differential equations. In these methods, a loss function for training a deep neural network is formulated, so that differential operators, boundary conditions, and initial conditions of the intended partial differential equation are satisfied. This study applied a deep learning-based method to solve viscous and resistive magnetohydrodynamic (MHD) equations. In particular, the deep learning-based method is applied to the 1D Brio-Wu shock wave problem, 2D Balsara-Spicer MHD Rotor problem, 2D Orszag-Tang MHD Vortex problem, and 2D magnetosphere problem. The approximated solution obtained by the deep learning-based method generally agrees with that obtained by conventional numerical methods.