Physics Informed Machine Learning of Smooth Particle Hydrodynamics: Solving Inverse Problems using a mixed mode approach

While modern machine learning tools have been successfully applied to many fluid dynamics applications, including Smooth Particle Hydrodynamics (SPH), it still remains a great challenge to encode underlying physical structure into machine learning algorithms. In this work we show how a mixed mode approach (using both forward and reverse mode automatic differentiation) along with classical analytic techniques, such as the adjoint method, can be used to solve inverse problems for SPH (in both physical parameter space and function space). In addition, our mixed mode approach allows us to introduce the physical (and numerical) structure of SPH into the machine learning algorithm which can be used to learn a fully parameterized SPH model from Lagrangian flow data.