Can I read Learning Thermodynamically Stable and Galilean Invariant Partial Differential Equations for Non-Equilibrium Flows on EtoBox?

Learning Thermodynamically Stable and Galilean Invariant Partial Differential Equations for Non-Equilibrium Flows by Juntao Huang; Zhiting Ma; Yizhou Zhou; Wen-An Yong is a Engineering article available to read on EtoBox.

What is Learning Thermodynamically Stable and Galilean Invariant Partial Differential Equations for Non-Equilibrium Flows about?

## Abstract 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 equations for non-equilibrium flows in one dimension, the learned PDEs are parameterized by fully connected neural networks and satisfy the conservation-dissipation principle automatically. In particular, they are hyperbolic balance laws and Galilean invariant. The training data are generated from a kinetic model with smooth initial data. Numerical results indicate that the learned PDEs can achieve good accuracy in a wide range of Knudsen numbers. Remarkably, the learned dynamics can give satisfactory results with randomly sampled discontinuous initial data and Sod’s shock tube problem although it is trained only with smooth initial data.

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

Author

Juntao Huang; Zhiting Ma; Yizhou Zhou; Wen-An Yong

Publisher

Walter de Gruyter GmbH

Published

2021

Language

EN

Field

Engineering (Physical Sciences)