Numerical Analysis and Computation Commons^™

Numerical Approximations Of Phase Field Equations With Physics Informed Neural Networks, Colby Wight

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Designing numerical algorithms for solving partial differential equations (PDEs) is one of the major research branches in applied and computational mathematics. Recently there has been some seminal work on solving PDEs using the deep neural networks. In particular, the Physics Informed Neural Network (PINN) has been shown to be effective in solving some classical partial differential equations. However, we find that this method is not sufficient in solving all types of equations and falls short in solving phase-field equations. In this thesis, we propose various techniques that add to the power of these networks. Mainly, we propose to embrace the …