Physics-Informed Neural Networks: Addressing Optimisation Challenges
Supervisor: Dr Tiffany Vlaar
School: Mathematics & Statistics
Description:
Machine learning methods offer a promising alternative to traditional solvers for problems involving partial differential equations (PDEs), but do not inherently respect the underlying physics of the problem. Physics-informed neural networks (PINNs) [Raissi et al., 2019] are neural networks that explicitly take into account the physical domain knowledge. PINNs have found success in various science and engineering domains (such as e.g. climate modeling, molecular dynamics, and geosciences), but face various training challenges, which affect their accuracy and robustness. This project will introduce the student to the formulation of PINNs and their deployment. Background in machine learning will be provided as needed. The student will then study and characterise problems observed in PINN optimisation and how these are reflected in the optimisation landscape. By exploiting developed understanding on the important roles played by the choice of initialisation and regularisation, the student will then work towards addressing identified issues.