论文标题
学习热力学稳定和非平衡流动的galieran偏微分方程
Learning Thermodynamically Stable and Galilean Invariant Partial Differential Equations for Non-equilibrium Flows
论文作者
论文摘要
在这项工作中，我们开发了一种基于不可逆热力学的保护 - 弥散形式主义，以学习可解释，热力学稳定和伽利亚不变的部分微分方程（PDE）。作为一个在一个维度上的非平衡流的管理方程式，学到的PDE被完全连接的神经网络参数化，并自动满足保护渗透原理。特别是，它们是双曲线平衡法律和伽利略不变的。训练数据是由具有平滑初始数据的动力学模型生成的。数值结果表明，学到的PDE可以在广泛的Knudsen数字中获得良好的精度。值得注意的是，学到的动态可以通过随机采样的不连续数据和SOD的冲击管问题给出令人满意的结果，尽管仅通过平滑的初始数据进行训练。
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.
