Dominic Bair (Dept. of Mathematical Sciences, MSU) - Master's Thesis Defense

04/14/2022  3:10pm

Abstract:

Use of data-driven techniques to solve PDEs is a rapidly developing field. Current deep learning methods can find solutions to high-dimensional PDEs with great accuracy and efficiency.  However, for certain classes of problems these techniques may be inefficient. We focus on PDEs with a so-called "variational formulation". Here the solution to the PDE is represented as a minimizer or maximizer to a functional. We propose a novel deep learning algorithm to find these minimizers with similar accuracy and greater efficiency than techniques using the PDE formulation. We call this "Deep Variational Methods" (DVM).