应兰州大学数学与统计学院杨志鹏副教授邀请，同济大学数学科学学院孙琪助理教授将于2025年06月05日上午做学术报告，欢迎全校师生参加。

报告题目：Physics-Informed Machine Learning with Embedded Domain Knowledge

时间：2025年06月05日(星期四)上午09:00-10:00

地点：腾讯会议981-940-611，密码112233

报告摘要：Physics-Informed neural networks have emerged as a powerful tool in scientific machine learning, providing efficient numerical solutions for broad classes of partial differential equations. However, conventional learning approaches often struggle to resolve problems involving singular behaviors, such as discontinuities in hyperbolic equations or singularities in Green’s functions. In this talk, knowledge-embedded neural networks are introduced to address these challenges, which comprise three innovative components:

(1)incorporating domain-specific prior knowledge into the solution ansatz by including an augmented variable;

(2)utilizing neural networks to handle the increased dimensionality and address both linear and nonlinear problems within a unified mesh-free learning framework;

(3)projecting the trained model back onto the original physical domain to obtain the approximate solution.

With collocation points sampled only on piecewise surfaces rather than fulfilling the whole lifted space, we demonstrate through numerical benchmarks that our methods can efficiently resolve solution singularities in both hyperbolic and elliptic problems.

报告人简介

孙琪，2013年本科毕业于中国科学技术大学，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学院并担任助理教授职位。研究内容主要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身份发表于SISC、JCP、SINUM、CiCP和NMPDE等国内外知名期刊，主持国自然青年基金并参与多项科研项目。

数学与统计学院

甘肃应用数学中心

萃英学院

2025年6月3日