报告题目:VC-PINN: variable coefficient physics-informed neural network for forward and inverse problems of PDEs with variable coefficient

报告人：陈勇 教授（华东师范大学）

报告时间：2023年10月6日（周五）17:00-18:00

报告地点：仁和106

摘要：The paper proposes a deep learning method specifically dealing with the forward and inverse problem of variable coefficient partial differential equations – Variable Coefficient Physics-Informed Neural Network (VC-PINN). The shortcut connections (ResNet structure) introduced into the network alleviates the “van- ishing gradient” and unify the linear and nonlinear coefficients. The developed method was applied to four equations including the variable coefficient Sine-Gordon (vSG), the generalized variable coefficient Kadomt- sev–Petviashvili equation (gvKP), the variable coefficient Korteweg-de Vries equation (vKdV), the variable coefficient Sawada-Kotera equation (vSK). Numerical results show that VC-PINN is successful in the case of high dimensionality, various variable coefficients (polynomials, trigonometric functions, fractions, oscillation attenuation coefficients), and the coexistence of multiple variable coefficients. We also conducted an in-depth analysis of VC-PINN in a combination of theory and numerical experiments, including four aspects: the necessity of ResNet; the relationship between the convexity of variable coefficients and learning; anti-noise analysis; the unity of forward and inverse problems/relationship with standard PINN.

报告人简历：陈勇，华东师范大学，博士生导师，计算机理论所所长，上海市闵行区拔尖人才。长期从事非线性数学物理、可积系统、计算机代数及程序开发、可积深度学习算法，混沌理论、大气和海洋动力学等领域的研究工作。提出了一系列可以机械化实现非线性方程求解的方法，发展了李群理论并成功应用于大气海洋物理模型的研究.提出可积深度学习算法，开发出一系列可机械化实现的非线性发展方程的研究程序。已在SCI收录的国际学术期刊上发表SCI论文300余篇，引用7000余篇次。主持国家自然科学基金面上项目4项，国家自然科学基金重点项目2项(第一参加人和项目负责人)、973项目1项(骨干科学家)、国家自然科学基金长江创新团队项目2项(PI)。

邀请人：沈守枫 教授