Introduction
This bi-monthly seminar series explores real-world applications of physics-informed machine learning (Φ-ML) methods to the engineering practice. They cover a wide range of topics, offering a cross-sectional view of the state of the art on Φ-ML research, worldwide.
Participants have the opportunity to hear from leading researchers and learn about the latest developments in this emerging field. These seminars also offer the chance to identify and spark collaboration opportunities.
About the event
We explore challenges in training Physics-Informed Neural Networks (PINNs), emphasizing the role of the loss landscape in the training process. We examine difficulties in minimizing the PINN loss function, particularly due to ill-conditioning caused by differential operators in the residual term. We compare gradient-based optimizers Adam, L-BFGS, and their combination Adam+L-BFGS, showing the superiority of Adam+L-BFGS, and introduce a novel second-order optimizer, NysNewton-CG (NNCG), which significantly improves PINN performance. Theoretically, our work elucidates the connection between ill-conditioned differential operators and ill-conditioning in the PINN loss and shows the benefits of combining first- and second-order optimization methods. Our work presents valuable insights and more powerful optimization strategies for training PINNs, which could improve the utility of PINNs for solving difficult partial differential equations.
Watch on demand:
Recording will be uploaded after the seminar.
