汇报标题 (Title)：Informative Computing for Scientific Machine Learning
（科学机械进建中的信息推算）
汇报人 (Speaker)：孙琪 助理教授（同济大学）
汇报功夫 (Time)：2025年11月19日（周三）8:00
汇报地址 (Place)：校本部GJ303
约请人(Inviter)：李新祥
主办部门：理学院数学系
汇报提要：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.
