报告题目 (Title)：Informative Computing for Scientific Machine Learning
报告题目 (中文)：科学机器学习中的信息计算
报告人 (Speaker)： 孙琪 助理教授（同济大学）
报告时间 (Time)：2025年11月19日(周三) 8:00
报告地点 (Place)：校本部GJ303
邀请人(Inviter)：李新祥
报告摘要：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.