Date of Award

9-2023

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Department of Mathematics and Statistics

First Advisor

Benjamin F. Akers, PhD

Abstract

A machine learning procedure is proposed to create numerical schemes for solutions of certain types of nonlinear wave equations on coarse grids. This method trains stencil weights of a discretization of the equation, with the truncation error of the scheme as the objective function for training. A neural network is used as a model for the stencil weights. The method uses centered finite differences to initialize the optimization routine and a second-order implicit-explicit time solver as a framework. Symmetry conditions are enforced on the learned operator to ensure a stable method. The procedure is applied to the Korteweg - de Vries and nonlinear Schrödinger equations. It is observed to be more accurate than finite difference or spectral methods on coarse grids when the initial data is near enough to the training set.

AFIT Designator

AFIT-ENC-DS-23-S-004

Comments

A 12-month embargo was observed for posting this dissertation on AFIT Scholar.

Approved for public release. PA case number on file.

Additional Files
4. SF 298 - Williams.pdf (38 kB)
SF298 for AFIT-ENC-DS-23-S-004
Download

Share

COinS