报告题目 Title：Energy Equidistribution Moving Sampling Physics-informed Neural Networks for Solving Energy Conservative Partial Differential Equations

报告人 Speaker：张冉

报告人所在单位 Affiliation：上海财经大学

时间 Time：2026-09-24 16:00-17:00

地点 Venue：Room 1513, Guanghua Eastern Main Tower, Fudan University (Handan Campus)

报告摘要 Abstract：This talk presents a novel energy equidistribution adaptive sampling framework for multi-dimensional conservative PDEs, introducing both location-based and velocity-based formulations of energy equidistribution moving mesh PDEs (EMMPDEs). The framework utilizes the energy density function as the monitor function, ensuring that mesh adaptation dynamically tracks energy evolution during temporal integration. These theoretical developments are integrated with deep neural networks to establish the energy equidistribution Moving Sampling Physics-Informed Neural Networks (EEMS-PINNs), which integrate physics-informed learning with energy-adaptive mesh optimization.  Extensive numerical experiments demonstrate that EEMS-PINNs effectively maintain solution accuracy in long-time simulations while preserving conserved energy. The framework's robustness is further evidenced by its stable performance in non-conservative systems.

个人简介 Bio：张冉，上海财经大学数学学院副教授，博士生导师，博士毕业于复旦大学数学学院, 博士期间在德国哥廷根大学数值与应用数学研究所访问。研究方向为散乱数据拟合，径向基核函数，函数逼近理论以及数值算法优化等。在 Numerical Algorithms、Advances in Computational Mathematics 等国内外著名期刊发表论文数篇。主持或参与多项国家自然科学基金、国家重点项目。

海报 Poster: 张冉 学术报告.jpg