Physics-Informed Neural Networks for Modeling of Space Plasmas

The equations of magnetohydrodynamics (MHD) are a coupled set of partial differential equations describing the evolution of fluid properties (density, pressure, velocity) and magnetic fields. Determining an analytical solution for these equations is usually impossible, even for the simplest cases, such as single-fluid ideal MHD. Existing MHD solvers (such as GAMERA) typically utilize mesh-based techniques and a finite difference or finite element approach, which explicitly discretizes the equations. Finding the solution at a non-mesh point requires interpolation (which can be difficult for nonuniform meshes). A physics-informed neural network (PINN) can generate a mesh-free solution given only the form of the differential equations, and any required boundary or initial conditions. PINN solutions can be improved with the addition of data at any additional points within the domain or on the boundary. The same PINN approach can also be used for data-driven system identification: given the equations and any available data, the PINN can generate a solution while simultaneously estimating the values of the physical parameters of the system. We present examples of both of these techniques for the study of plasma wave phenomena.