学术报告20250928：A data-driven Integrable BFGS Algorithm (IBA-PDE) for discovering PDEs

报告题目：A data-driven Integrable BFGS Algorithm (IBA-PDE) for discovering PDEs

报告人：李彪 教授

报告摘要：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 discovering 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.

报告人简介：李彪，宁波大学数学与统计学院教授、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。获省部级二等奖和三等奖各1项；主持和参与国家自然科学基金面上项目和重点项目多项；作为主要参加人完成国家自然科学基金重点项目多项；在国内外重要刊物上发表SCI论文200余篇，他引五千多次；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”。

报告时间：2025年9月28日8：30—9：00

报告地点：数学科学学院512会议室

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内蒙古大学数学科学学院

2025年9月27日