Deep Learning and Partial Differential Equations

Automated Finite Element Mesh Generation

Artificial Intelligence/Machine Learning/Deep Learning, Fluid Dynamics

Finite Element Methods (FEM) have been ubiquitously used in solving Partial Differential Equations (PDE) in an extremely wide range of fields in computer science and engineering, ranging from critical domains such as construction, material, fluid dynamics, to entertainments/education such as visual effects, computer graphics & animation and virtual reality. One key fundamental aspect to such research is a well-balanced trade-off between accuracy and speed, and a significant proportion of the effort has been devoted to generating high-quality and adaptive FEM meshes.

In the era of machine learning and deep learning, scientists have been actively exploring data-driven methods such as deep neural networks to help directly solve PDEs. However, we argue that there is a different route to this problem. We can combine traditional numerical solvers with smartly generated FEM meshes via deep learning. This way, we aim to both accelerate the speed and safeguard the accuracy. This route eliminates the worst-case scenarios where deep learning models can generate wrong predictions due to limited training data or the lack of model generalizability when used to predict the solutions directly.

The team has published a series of papers in deep learning-based FEM mesh generation including MeshingNet: A New Mesh Generation Method Based on Deep Learning and MeshingNet3D: Efficient Generation of Adapted Tetrahedral Meshes for Computational Mechanics. Given it is the inception of such research, we invite promising PhD candidates to work with us for further theoretical explorations and wider applications.