讲座时间：2024年1月15日上午8:20开始

讲座地点：总理楼605

讲座主办方：吉首大学数学与统计学院

讲座题目一：可积深度学习

讲座人：陈勇教授（华东师范大学数学科学学院）

讲座摘要：介绍非线性科学与计算机发展关系。探讨我们提出的可积深度学习的理论架构和发展方向。介绍我们可积深度学习的研究目前的进展。

讲座人简介：陈勇，华东师范大学，博士生导师，计算机理论所所长。长期从事非线性数学物理，计算机代数及程序开发、可积深度学习算法的研究工作. 提出了一系列可以机械化实现非线性方程求解的方法和可积深度学习算法，发展了李群理论，开发出一系列研究程序。已在SCI收录的国际学术期刊上发表SCI论文300余篇。主持和参加国家自然科学基金国家自然科学基金重点项目，973项目，国家自然科学基金长江创新团队项目，面上项目。

讲座题目二：Defocusing NLS equation with a nonzero background: Painleve asymptotics in two transition regions

讲座人：范恩贵教授（复旦大学数学科学学院）

  讲座摘要：We address the Painleve asymptotics of the solution in two transition regionsfor the defocusing nonlinear Schrodinger (NLS) equation with finite density initial data. The key to prove this result is the formulation and analysis of a Riemann-Hilbert problem associated with the Cauchy problem for the defocusing NLS equation. With the Dbar generalization of the Deift-Zhou nonlinear steepest descent method and double scaling limit technique, in two transition regions, we find that the leading order approximation to the solution of the defocusing NLS equation can be expressed in terms of the Hastings-McLeod solution of the Painleve II

讲座人简介：范恩贵，复旦大学、博士生导师,主要研究方向：可积系统和反散射理论；主持国家自然科学基金、上海曙光计划等多项研究课题。 在 《Adv. Math.》、 《Comm. Math. Phys.》、《SIAM J. Math. Anal.》、《J. Diff. Equ.》等国际重要期刊发表论文150余篇。应邀访问美国密苏里大学、密西根州立大学、德克萨斯大学、日本京都大学、香港大学等。曾获教育部自然科学二等奖、上海市自然科学二等奖、复旦大学谷超豪数学奖。

讲座题目三：On existence of global solutions to the nonlocal Hirota equation on the line

讲座人：田守富教授（中国矿业大学数学学院）

讲座摘要：In this talk, we report that the existence of global solutions to the Cauchy problem of the nonlocal Hirota equation is obtained on the line with the small-norm assumption on initial data H3(R)H1,1(R). The Lipschitz continuity of the eigenfunctions and reflection coefficients on the initial data is considered to offer a priori estimation for the solution of nonlocal Hirota equation. By using the reconstruction formula and estimation of the time-dependent RH problem, the existence of a unique global solution to the nonlocal Hirota equation related to the Cauchy problem is ultimately obtained.

讲座人简介：田守富，中国矿业大学数学学院教授、博士生导师，2012年博士毕业于大连理工大学数学科学学院，主要从事可积系统、反散射理论、Riemann-Hilbert问题等的研究；主持国家自然科学基金面上项目等多项研究课题；研究成果在《Adv. Math.》、《Math. Ann.》、《Annales Henri Poincaré》、《J. Differential Equations》和《中国科学》等国内外期刊上发表学术论文多篇； 曾获辽宁省自然科学二等奖、淮海科技二等奖、淮海科技英才奖、江苏省工业与应用数学学会青年科技奖和江苏省数学学会优秀论文奖等；入选国家高层次青年人才计划、江苏省“333工程”中青年科学技术带头人、江苏省“六大人才高峰”高层才人才计划和2021-2023连续三年爱思唯尔中国高被引学者等。

讲座题目四：Whitham modulation theory and Riemann problem of the Gerdjikov-Ivanov equation

讲座人：王灯山教授（北京师范大学数学科学学院）

讲座摘要：We develop the Whitham theory to study the Riemann problem of the Gerdjikov-Ivanov equation that describes the photon fluid with quintic nonlinearity. The one-phase periodic solution of the Gerdjikov-Ivanov equation and the corresponding Whitham equation are derived by the finite gap integration method. Subsequently, the main basic wave structures arising from the discontinuous initial-value conditions are found by distinguishing the distributions of the Riemann invariants. Some exotic optical undular bores are observed by classifying the solutions of the Riemann problem of the Gerdjikov-Ivanov equation. It is observed that the analytical results from Whitham theory are in excellent agreement with the numerical solutions.

讲座人简介:王灯山，北京师范大学数学科学学院，教授、博士生导师。主要从事可积系统和渐近分析方面的研究，在Analysis & PDE, Physical Review Letters, J. Differential Equations, J. Nonlinear Science 和Physica D等国际期刊发表学术论文90余篇，主持国家自然科学基金面上项目等国家级和省部级项目10余项，曾获北京市自然科学奖二等奖(第一完成人)和茅以升北京青年科技奖，并参与获得北京市科学技术奖一等奖。入选北京市“科技新星”计划、北京市“高创计划”青年拔尖人才、北京市“长城学者”计划以及爱思唯尔2020-2022年中国高被引学者。

讲座题目五：Mix-training physics-informed neural networks for the rogue waves of nonlinear Schrödinger equation

讲座人：李彪教授（宁波大学数学与统计学院）

讲座摘要：In this paper, we propose mix-training physics-informed neural networks (PINNs). This is a deep learningmodel with more approximation ability based on PINNs, combined with mixed training and prior information.We demonstrate the advantages of this model by exploring rogue waves with rich dynamic behavior in thenonlinear Schrödinger (NLS) equation. Compared with the original PINNs, numerical results show that thismodel can not only quickly recover the dynamical behavior of the rogue waves of NLS equation, but alsoimprove its approximation ability and absolute error accuracy significantly, and the prediction accuracy hasbeen improved by two to three orders of magnitude. In particular, when the space–time domain of the solution
expands, or the solution has a local sharp region, the proposed model still has high prediction accuracy.

讲座人简介：李彪，宁波大学数学与统计学院教授，博导。主要从事非线性数学物理，可积系统及应用，深度学习等方面的研究。主持与参与国家自然科学基金重点项目，面上项目,省部级项目10余项，发表论文SCI论文100余篇，他引3千多次。入选浙江省“151”人才工程和宁波市“4321”人才工程。