Department of Mathematical Sciences
Taorui Wang, WPI
Monday, March 23rd, 2026
2:00PM-2:50PM
Stratton Hall 202
Speaker: Taorui Wang, WPI
Title: Continual Learning with Multi-Stage Correction for PINNs in Sharp-Transition PDEs
Abstract: Physics-informed neural networks often face significant difficulty when solving partial differential equations whose solutions contain sharp transition layers, including boundary layers, internal layers, and shock-like structures. In this talk, we introduce a continual-learning framework with multi-stage correction for this class of problems. Starting from easier regimes, the method progressively transfers learned information to more challenging parameter settings, and then applies successive correction stages to improve the approximation where sharp features remain unresolved. By combining warm-start continuation, scale-aware features, and localized correction mechanisms, the proposed approach aims to improve both training stability and solution accuracy for sharp-transition PDEs. Several numerical examples are presented to demonstrate the effectiveness of the framework.