主持人：朱升峰 教授
报告简介：
In this work, we propose the Adaptive Feature Capture Method (AFCM), a novel machine learning framework that adaptively redistributes neurons and collocation points in high-gradient regions to enhance local expressive power. Inspired by adaptive moving mesh techniques, AFCM employs the gradient norm of an approximate solution as a monitor function to guide the reinitialization of feature function parameters. This ensures that partition hyperplanes and collocation points cluster where they are most needed, achieving higher resolution without increasing computational over- head. The AFCM extends the capabilities of RFM to handle PDEs with near-singular solutions while preserving its mesh-free efficiency. Numerical experiments demonstrate the method’s effectiveness in accurately resolving near-singular problems, even in complex geometries. By bridging the gap between adaptive mesh refinement and randomized neural networks, AFCM offers a robust and scalable approach for solving challenging PDEs in scientific and engineering applications.
主讲人简介：
王筱平教授，1984年毕业于北京大学数学系，1990年从库朗数学研究所（NYU）获得博士学位。他曾在伯克利的数学研究所（MSRI）和科罗拉多大学担任博士后。1994年后历任香港科技大学数学系助理教授，副教授，教授，讲座教授及系主任。他是香港工业与应用数学学会首任主席。他于2007年获得冯康科学计算奖，是2016年SIAM材料科学数学会议2019年国际工业和应用数学大会的大会报告人，教育部长江学者讲座教授，中国工业与应用数学学会会士和广东省珠江杰出人才。现为香港中文大学理工做爱视频校长讲座教授。
