Learning Thermodynamically Stable and Galilean Invariant Partial Differential Equations for Non-equilibrium Flows
arXiv:2009.13415 · doi:10.1515/jnet-2021-0008
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.
References in corpus (10)
- Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
- Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics
- DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics
- Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations
- PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network
- Non-invasive Inference of Thrombus Material Properties with Physics-informed Neural Networks
- Uniformly Accurate Machine Learning Based Hydrodynamic Models for Kinetic Equations
- OnsagerNet: Learning Stable and Interpretable Dynamics using a Generalized Onsager Principle
- Machine learning based non-Newtonian fluid model with molecular fidelity
- Properties of Conservation-dissipation Formalism of Irreversible Thermodynamics