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Journal of Computational Physics

• Spacetime control volume PINN reformulation naturally handles IC/BC and conservation. • Novel biases for entropy consistency and TVD provide robust DNN modeling of shocks. • Thermodynamic consistency allows extraction of black box EOS models from data. • EOS extracted for gas + metals in extreme environments from DSMC/MD data. Physics-informed neural network architectures have emerged as a powerful tool for developing flexible PDE solvers that easily assimilate data. When applied to problems in shock physics however, these approaches face challenges related to the collocation-based PDE discretization underpinning them. By instead adopting a least squares space-time control volume scheme, we obtain a scheme which more naturally handles: regularity requirements, imposition of boundary conditions, entropy compatibility, and conservation, substantially reducing requisite hyperparameters in the process. Additionally, connections to classical finite volume methods allows application of inductive biases toward entropy solutions and total variation diminishing properties. For inverse problems in shock hydrodynamics, we propose inductive biases for discovering thermodynamically consistent equations of state that guarantee hyperbolicity. This framework therefore provides a means of discovering continuum shock models from molecular simulations of rarefied gases and metals. The output of the learning process provides a data-driven equation of state which may be incorporated into traditional shock hydrodynamics codes.

Thermodynamically consistent physics-informed neural networks for hyperbolic systems