报告题目1：Lax pairs informed neural networks solving integrable systems

报告人：陈勇教授，华东师范大学

报告时间：2024年6月27日（周四）15:00-15:50

报告地点：20-200

报告摘要：We propose the Lax pairs informed neural networks (LPINNs) tailored for integrable systems with Lax pairs by designing novel network architectures and loss functions, comprising LPINN-v1 and LPINN-v2. The most noteworthy advantage of LPINN-v1 is that it can transform the solving of complex integrable systems into the solving of a simpler Lax pairs to simplify the study of integrable systems, and it not only efficiently solves data-driven localized wave solutions, but also obtains spectral parameters and corresponding spectral functions in Lax pairs. On the basis of LPINN-v1, we additionally incorporate the compatibility condition/zero curvature equation of Lax pairs in LPINN-v2, its major advantage is the ability to solve and explore high-accuracy data-driven localized wave solutions and associated spectral problems for all integrable systems with Lax pairs. The numerical experiments in this work involve several important and classic low-dimensional and high-dimensional integrable systems, abundant localized wave solutions and their Lax pairs. The innovation of this work lies in the pioneering integration of Lax pairs informed of integrable systems into deep neural networks, thereby presenting a fresh methodology and pathway for investigating data-driven localized wave solutions and spectral problems of Lax pairs. 

报告人简介：陈勇，华东师范大学数学科学学院教授，博导，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、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，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，提出了可积深度学习框架。已在SCI收录的国际学术期刊上发表论文280篇。发表论文的SCI引用4000余篇次。主持国家自然科学基金面上项目3项，参与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团队项目2项(骨干成员)。

报告题目2：Nonlinear Waves: Formation and Dynamics

报告人：闫振亚研究员，中科院数学与系统科学研究院

报告时间：2024年6月27日（周四）15:55-16:40

报告地点：20-200

报告摘要：First of all, we introduce several types of nonlinear waves appearing many fields of nonlinear science, such as ocean, nonlinear optics, quantum mechanics, Bose-Einstein condensates, finance, etc. Secondly, we study the formation and dynamics of some significant nonlinear waves (e.g., peakons, rogue waves, quantum droplets) in the generalized NLS/GP equations with complex/real potentials via the analytical and numerical methods as well as deep learning.  Finally, we discuss some problems.

报告人简介：闫振亚，中科院数学与系统科学研究院研究员，全国百篇优秀博士论文获得者，荣获中国科学院2008年卢嘉锡青年人才奖，北京市科学技术二等奖。研究方向为复杂非线性波、可积性、符号分析等。