Physics Informed Machine Learning with Smoothed Particle Hydrodynamics: Compressiblity and Shocks*

Many formulations of Smoothed Particle Hydrodynamics (SPH) have been developed for handling compressible flows, such as those seen in astrophysics and engineering applications. Often, these formulations are first tested and developed on simple 1D and 2D shock problems in order to validate the modeling and numerical implementations. Nevertheless, the parameters of the formulation are usually adjusted in an ad-hoc manner, by trial and error. In this work, we explore the physics informed machine learning methods developed in [Woodward et al, arxiv:2110.13311, 2021], but using a compressible SPH formulation, to learn the SPH parameters to model shock waves. The formulation is verified against analytic solutions such as the 1D Sod and 2D Taylor-Sedov problems. Specifically, combining deep learning, automatic differentiation, and local sensitivity analysis, learn-able and parameterized compressible SPH formulations are constructed and fit to the analytical solutions of 1D and 2D shocks. These parameterizations are used to learn new parameterized smoothing kernels and artificial viscosity terms, with the goal of improving the SPH framework with respect to accuracy and modeling.