Solving Navier-Stokes equations in protoplanetary disk using physics-informed neural networks

Abstract

We show how physics-informed neural networks can be used to solve compressible \NS equations in protoplanetary disks. While young planets form in protoplanetary disks, because of the limitation of current techniques, direct observations of them are challenging. So instead, existing methods infer the presence and properties of planets from the disk structures created by disk-planet interactions. Hydrodynamic and radiative transfer simulations play essential roles in this process. Currently, the lack of computer resources for these expensive simulations has become one of the field's main bottlenecks. To solve this problem, we explore the possibility of using physics-informed neural networks, a machine learning method that trains neural networks using physical laws, to substitute the simulations. We identify three main bottlenecks that prevent the physics-informed neural networks from achieving this goal, which we overcome by hard-constraining initial conditions, scaling outputs and balancing gradients. With these improvements, we reduce the relative L2 errors of predicted solutions by 97% ~ 99\% compared to the vanilla PINNs on solving compressible NS equations in protoplanetary disks.