报告题目:A two-stage physics-informed neural network method based on conserved quantities and applications in localized wave solutions

报告人：陈勇 教授 (华东师范大学)

报告时间：2022年10月27日下午 18:30-19:30

报告地点：朝晖校区 教411

报告摘要：With the advantages of fast calculating speed and high precision, the physics-informed neural network method opens up a new approach for numerically solving nonlinear partial differential equations. Based on conserved quantities, we devise a two-stage PINN method which is tailored to the nature of equations by introducing features of physical systems into neural networks. Its remarkable advantage lies in that it can impose physical constraints from a global perspective. In stage one, the original PINN is applied. In stage two, we additionally introduce the measurement of conserved quantities into mean squared error loss to train neural networks. This two-stage PINN method is utilized to simulate abundant localized wave solutions of integrable equations. We mainly study the Sawada-Kotera equation as well as the coupled equations: the classical Boussinesq-Burgers equations and acquire the data-driven soliton molecule, M-shape double-peak soliton, plateau soliton, interaction solution, etc. Numerical results illustrate that abundant dynamic behaviors of these solutions can be well reproduced and the two-stage PINN method can remarkably improve prediction accuracy and enhance the ability of generalization compared to the original PINN method.

报告人简介：陈勇，华东师范大学，博士生导师，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。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3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：马立媛