活动时间：2025-07-15 16:00

活动地点：腾讯会议 455-965-540

主讲人：李彪 教授

主讲人中文简介：

李彪，宁波大学绅士漫画 教授、博士生导师，长期从事非线性数学物理、可积系统、深度学习算法、计算机符号和数值计算等领域的研究工作。参与获省部级二等奖和三等奖各1项；主持完成国家自然科学基金项目4项、省部级项目3项； 作为主要参加人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。 在国内外重要刊物上发表SCI论文200余篇，他引5千多次，2022年以来连续入选美国斯坦福大学和爱思唯尔数据库发布的《全球前2％顶尖科学家榜单》和“终身科学影响力排行榜”。

活动内容摘要：

Data-driven discovery of partial difference equations (PDEs) has become a hot topic, and scholars have proposed some excellent data-driven methods (PINNs,PDE-FIND,DLGA-PDE,SGA-PDE) and achieved good results in disIcovering PDEs. PINNs can only determine the coefficients of the PDE, rather than discovering the entire PDE through data. Other methods also have limitations in dealing with complex PDEs. This paper proposes a new integrable BFGS algorithm (IBA-PDE) for PDE discovery, which solves two key problems: (1) To manage the complexity and redundancy of candidate PDE terms, it incorporates a weight balance condition tailored for partially integrable PDEs, along with a preliminary optimization strategy, we first solve the problem of narrowing down the range of PDEs candidates; (2) To accurately estimate unknown PDEs coefficients, the method employs the BFGS optimization algorithm, enhancing the precision of the identification process. Through systematic numerical experiments, IBA-PDE demonstrates superior capability that not only rediscovers fundamental PDEs but also resolves previously intractable systems with unprecedented precision. Specifically, IBA-PDE discovered several complex integrable PDEs (fifth-order KdV, Kaup Kupershmidt, Sawada Kotera, complex modified KdV, Hirota, and (2+1) dimensional KP equations) and two non integrable PDEs (Burgers KdV and Chafee Infante equations), all of which have mean square errors (MSEs) of 10−9 and coefficien errors of almost zero. 

主持人：孙暄