Discontinuous Extreme Learning Machine for Interface and Free Boundary Problems

报告题目：Discontinuous Extreme Learning Machine for Interface and Free Boundary Problems

报 告 人：赵文举 副教授 博导 山东大学

报告时间：2025年11月27日14:00—17:30

报告形式：腾讯会议

会议ID： 831-693-144

报告摘要：Interface and free boundary problems arise in many scientific and engineering applications, where handling non-smooth behavior across interfaces remains a major challenge. While recent machine learning methods have shown promise for interface problems with known boundaries, extending them to free boundary settings is significantly harder due to computational complexity and structural limitations. Consequently, high-accuracy machine learning approaches for free boundary problems are still limited. In this talk, we present a new mesh-free method based on the locELM framework—a discontinuous extreme learning machine (DELM). By introducing an artificial discontinuity mechanism to capture interface non-smoothness, DELM achieves high accuracy and efficiency with far fewer parameters. The method also integrates naturally with front-tracking strategies, which enables a straightforward extension to free boundary problems. Numerical results for interface and Stefan problems illustrate the method’s accuracy, robustness, and scalability.

报告人简介：

赵文举，山东大学数学学院副教授，博士研究生导师，博士毕业于美国佛罗里达州立大学，主要研究方向包括随机型与确定型偏微分方程的数值解法、随机最优控制、计算流体力学及形状优化等。在CSIAM-AM, ESAIM: M2AN, SIAM SISC, JSC, JCP, JCM, IMAJNA，CICP, CMAME等国内外重要学术刊物发表论文30余篇，先后参与主持科技部重点研发计划、国家重点项目、山东省重大基础研究等多项科研课题。