题目：A machine learning method for solving PDEs with a robust initial learning rate

主讲人：李晓丽 教授

时间：2026年5月30日（星期六）16：00

地点：理学院308会议室

主办单位：理学院

主讲人简介：

李晓丽，山东大学教授，博士生导师，国家高层次青年人才入选者，山东省杰青，山东大学杰出中青年学者。担任中国数学会计算数学分会常务理事，CSIAM油水资源数值方法专委会秘书长。主要研究领域为偏微分方程数值解与计算流体力学。在SINUM, SISC, MCOM, JFM, M3AS, CMAME, JCP等计算数学高水平期刊上发表学术论文多篇。主持国家自然科学基金面上项目、重点项目子课题、青年项目等多个国家及省部级项目。

摘要：

In this talk, we develop two effective and stable methods for solving PDEs by introducing the new Lagrange multiplier-based subspace approach. The main idea is to view the optimization process of the loss function as an energy descent process for the gradient flow model. The constructed schemes first utilize the Lagrange multiplier method for preliminary optimization to identify subspaces that effectively capture the solution structure. Subsequently, the approximate solutions are obtained within these subspaces using the least squares approach. Numerical experiments demonstrate that our methods not only achieve high prediction accuracy but also exhibit robustness with respect to the initial learning rate.