偏微分方程系列报告

报告题目: Learning Galilean Invariant and Thermodynamically Stable PDEs for Non-equilibrium Flows

报告人:   雍稳安 教授 （清华大学）

报告摘要：

In this talk, I will present a method for learning thermodynamically stable and Galilean invariant PDEs. As governing equations for non-equilibrium flows in one dimension, the learned PDEs are parameterized by fully-connected neural networks and satisfies a certain thermodynamical stability criterion 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. 

报告人简介： 雍稳安，清华大学周培源应用数学中心研究员，博士生导师，博士毕业于德国海德堡大学，随后在苏黎世联邦理工学院做博士后，在海德堡大学获德国教授资格。雍稳安教授主要研究带有松弛的一阶偏微分方程组，对这种类型的方程组建立了系统的数学理论，创立了非平衡态热力学的守恒耗散理论（CDF），提出迄今唯一正确描述可压缩粘弹性流体流动的数学方程，建立了格子波尔茨曼方法（LBM）的稳定性。相关论文发表在ARMA，C. PDE, SIAM系列，JDE等国际一流杂志。

报告时间: 2021.5.13(周四) 下午 4:00-5:30

报告地点: 逸夫楼1537