Optimization Methods for Dynamic Mode Decomposition of Nonlinear Partial Differential Equations

Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations. Naturally, reduced-order modeling techniques come at the price of either computational accuracy or computation time. Optimization techniques are studied to improve either or both of these objectives and decrease the total computational cost of the problem. This thesis focuses on the dynamic mode decomposition (DMD) applied to nonlinear PDEs with periodic boundary conditions. It provides one study of an existing optimization framework for the DMD method known as the Optimized DMD and provides another study of a newly proposed optimization framework for the DMD method called the Split DMD.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2021

Author dc:creator

• Zigic, Jovan

Chair dc:contributor.committeechair

• Borggaard, Jeffrey T.

Committee members dc:contributor.committeemember

• Zietsman, Lizette
• Lin, Tao

• Optimization
• Model Order Reduction
• Partial Differential Equations

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:31161

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/103862