Homotopy Dynamics for Neural Networks in Solving Partial Differential Equations

：杨雅鸿（美国宾夕法尼亚州立大学）
：2025-05-21 10:30
：海韵园行政楼C503

报告人：杨雅鸿（美国宾夕法尼亚州立大学）

时  间：2025年5月21日10:30

地  点：海韵园行政楼C503

内容摘要:

Solving partial differential equations (PDEs) using neural networks has become a famous topic in scientific machine learning. However, training neural networks remains challenging due to the highly complex and non-convex energy landscapes of the associated loss functions. These difficulties are further amplified in sharp interface problems, where certain parameters in the PDEs introduce near-singularities in the loss. In this talk, I will present a novel training framework based on homotopy dynamics to address these challenges. Specifically, I will introduce two homotopy strategies: the first performs homotopy in the activation functions by gradually transforming from simpler to the original nonlinearities; the second applies homotopy in the PDE parameters to manage the singular behavior in sharp interface regimes. Both approaches demonstrate improved training stability and enhanced accuracy in capturing sharp interfaces when solving PDEs with neural networks.

个人简介：

Dr. Yahong Yang earned his Ph.D. in Mathematics from the Hong Kong University of Science and Technology in 2023 and is currently a Postdoctoral Researcher at Pennsylvania State University. In August 2025, he will join the Georgia Institute of Technology as a Visiting Assistant Professor. His research interests span machine learning theory, mathematical modeling in materials science and biology, and numerical methods for solving partial differential equations. Dr. Yang has published in leading journals—including the SIAM Journal on Multiscale Modeling & Simulation, the Journal of Computational Physics, and the Journal of Scientific Computing—and has presented his work at top conferences in machine learning such as NeurIPS and ICML. His current research focuses on advancing deep learning theory and applying machine-learning techniques to complex PDEs, with applications to models like the Allen–Cahn equation, the Gray–Scott reaction–diffusion system, and Green’s functions.

 

联系人：陈黄鑫