报告题目：Informative Computing for Scientific Machine Learning

报告人：孙琪  复旦大学

报告时间：11月24日 4:00

报告地点：五教5405

摘要：

Physics-Informed machine learning has emerged as a powerful paradigm in scientific computing, providing effective surrogate solutions and operators for broad classes of partial differential equations. However, conventional learning approaches often struggle with problems involving singular behaviors, such as discontinuities in hyperbolic equations or singularities in Green’s functions. This talk introduces an informative computing framework that addresses these challenges through three innovations: (1) incorporating domain-specific prior knowledge into the solution ansatz via an augmented variable;  (2) utilizing neural networks to handle the increased dimensionality in a mesh-free manner;  (3) reconstructing solutions or operators by projecting trained models back onto the physical domain. With collocation points sampled only on piecewise hyperplanes rather than fulfilling the entire lifted space, we demonstrate through various benchmarks and applications that our methods efficiently resolve solution singularities in both hyperbolic and elliptic problems.

个人简介：

孙琪，2013年本科毕业于中国科学技术大学数学科学学院，随后在与中国工程物理研究院的联合培养下获得博士学位，期间赴美国哥伦比亚大学留学两年。2019-2021年获得北京大学博雅博士后资助，随后加入同济大学数学科学学院并担任助理教授职位。研究内容集中于偏微分方程数值解、不确定性量化、最优控制理论与机器学习的交叉领域，相关成果以第一作者或通讯作者的身份发表于 SISC、SINUM、JCP、CiCP 和 NMPDE 等国内外知名期刊，主持一项国家自然科学基金青年基金。