PI Seminar Series: Operator Preconditioning Perspective on training PINNs скачать в хорошем качестве

PI Seminar Series: Operator Preconditioning Perspective on training PINNs

Welcome to the Param-Intelligence (PI) Seminar Series, led by Dr. Ameya D. Jagtap. Dr. Emmanuel de Bézenac from INRIA, France, gave a talk titled "An Operator Preconditioning Perspective on Training in Physics-Informed Machine Learning." He explored the challenges of training physics-informed machine learning models, particularly PINNs, by analyzing the behavior of gradient descent algorithms in minimizing PDE residuals. His findings highlighted that training difficulties arise due to the conditioning of a crucial differential operator; specifically, the Hermitian square of the PDE's underlying operator. Poor conditioning of this operator results in slow or ineffective optimization, which sheds light on fundamental limitations in PINN training.