江苏省应用数学（中国矿业大学）中心系列学术报告
报告题目：The data-driven discovery of partial differential equations by symbolic genetic algorithm
报告时间：2023年 11月16日11:40-12:20
报告人：李彪宁波大学教授、博士生导师
数学学院A302室 腾讯会议：会议 ID： 387-266-3917
摘要：This paper introduce a symbolic genetic algorithm (SGA) for discovering PDEs capable of independently deriving PDEs directly from data, devoid of prior knowledge regarding equation structure. Primarily, SGA employs a flexible symbol representation of PDEs, transforming these into a forest with each PDEs segment forming a binary tree. Subsequently, SGA utilizes a novel algorithm to update the node attributes of the tree, and optimizes the binary tree (the terms of PDEs), obtaining the definitive form. It is worth mentioning that SGA adopts sparse regression algorithm in error optimization and finite difference method in derivative approximation, combining traditional numerical method with modern method. In experiment, SGA successfully discover the Korteweg-de Vries (KdV) equation by two- and three-soliton solutions. Likewise, two kinds of nonlinear Schr¨odinger (NLS)
equations were accurately discoveried by two-soliton solution and second-order rogue waves. Using this algorithm, we can automatically match the corresponding differential equations based on partial data from existing solutions; Furthermore, in the future, applying this algorithm to partial data in physical, chemical, biological and other experiments is likely to automatically match known differential equations and even discover new ones, which is very meaningful.
报告人简介： 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。主持完成国家自然科学基金4项、省部级项目3项； 参与完成国家自然科学基金重点项目2项；现主持国家自然科学基金面上项目1项和参加国家自然科学基金重点项目1项。发表论文SCI论文100余篇，他引3千多次。