Physics Informed Machine Learning of Smooth Particle Hydrodynamics: Validation of the Lagrangian Turbulence Approach

Smooth particle hydrodynamics (SPH) is a mesh-free Lagrangian method for obtaining approximate numerical solutions of the equations of fluid dynamics, which has been widely applied to weakly- and strongly compressible turbulence in astrophysics and engineering applications. In this work, we develop a hierarchy of parameterized and learn-able SPH simulators, by mixing automatic differentiation (both forward and reverse mode) with forward and adjoint based sensitivity analyses. We show that our physics inspired learning method is capable of: (a) solving inverse problems over both the physically interperatable parameter space, as well as over the space of Neural Network functions; (b) learning Lagrangian statistics of turbulence; (c) combining trajectory based, probabilistic, and field based loss functions; and (d) extrapolating beyond training sets into more complex regimes of interest.