江蘇省應用數學（中國礦業大學）中心系列學術報告
報告題目：The data-driven discovery of partial differential equations by symbolic genetic algorithm
報告時間：2023年 11月16日11:40-12:20
報告人：李彪甯波大學教授、博士生導師
伟德bvA302室 騰訊會議：會議 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.
報告人簡介： 李彪 甯波大學數學與統計學院教授， 博導。主要從事非線性數學物理，可積系統及應用，深度學習等方面的研究。主持完成國家自然科學基金4項、省部級項目3項； 參與完成國家自然科學基金重點項目2項；現主持國家自然科學基金面上項目1項和參加國家自然科學基金重點項目1項。發表論文SCI論文100餘篇，他引3千多次。