BIMSA > Data Analysis and Problem Solving Seminar Data Analysis and Problem Solving Seminar Governing Equations in PIML
Governing Equations in PIML
Organizer
Xiaoming John Zhang
Speaker
Zhuoyang Zhao
Time
Friday, June 12, 2026 3:00 PM - 4:30 PM
Venue
A3-1-301
Online
Zoom 204 323 0165 (BIMSA)
Abstract
Physics-Informed Machine Learning (PIML) enforces physical laws by iteratively minimizing the strong-form residuals of governing equations. However, automatic differentiation (AD) faces significant computational and accuracy bottlenecks when handling high-order derivatives, high-dimensional problems, or complex operators. This presentation explores the latest algorithmic advances in handling governing equations within PIML. We highlight alternative derivative calculation strategies, such as Stochastic Dimension Gradient Descent (SDGD) for overcoming the curse of dimensionality. Furthermore, we detail the crucial roles of non-dimensionalization and mathematical reformulation in resolving optimization difficulties and simplifying loss constraints. Finally, we introduce the expansion of differential operators to include variational forms (vPINNs), fractional equations (fPINNs), and solver framework extensions for stochastic differential equations (SDEs). These advancements provide unprecedented scalability and robustness for solving complex physical systems.
Speaker Intro
Zhao Zhuoyang is a first-year Ph.D. student in a joint Program between BIMSA and Renmin University of China, majoring in Mathematics, under the supervision of Professor Zhang Xiaoming.