Learning Thermodynamically Stable and Galilean Invariant Partial Differential Equations for Non-Equilibrium Flows

In this work, we develop a method for learning interpretable, thermodynamically stable and Galilean invariant partial differential equations (PDEs) based on the Conservation-dissipation Formalism of irreversible thermodynamics. As governing non-equilibrium flows in one dimension, learned PDEs are parameterized by fully-connected neural networks satisfy conservation-dissipation principle automatically. particular, they hyperbolic balance laws invariant. The training data generated from kinetic model with smooth initial data. Numerical results indicate that can achieve good accuracy wide range Knudsen numbers. Remarkably, dynamics give satisfactory randomly sampled discontinuous Sod's shock tube problem although it is trained only