PINNs -- Multi-Fidelity Physics-Informed Neural Network to Solve Partial Differential Equations

Research Project, 2023 – 2027

Partial Differential Equations (PDEs) are widely used to describe different physical phenomena, such as fluid dynamics and ocean wave evolution. Current CFD methods for high-fidelity solutions of PDEs in fluid dynamics require large meshes with fine resolution and short time steps. The solutions of the stochastic PDEs that describe the dynamics of ocean wave evolution strongly depend on the resolution of the spatial and temporal discretization of the ocean environment. Both these sets of PDEs are normally solved by either numerical or empirical methods with multiple approximations and different levels of fidelity/resolution. The fast development of various Machine Learning (ML) algorithms provides opportunities to build explicit/black-box models in terms of pre-defined boundary and initial conditions.

The main aim of this project is to exploit the recent developments in machine learning and multi- fidelity deep learning algorithms to accelerate and improve the efficiency of PINNs. The current study will answer the research question of how to efficiently and accurately solve PDEs that describe fluid dynamics and wave evolutions by combining PINNs and multi-fidelity algorithms. That is what the cover picture of the proposal is illustrating.