Show simple item record

dc.contributor.advisorChairperson, Graduate Committee: Dominique Zossoen
dc.contributor.authorBair, Dominic Roberten
dc.description.abstractThe 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 family of novel deep learning algorithms to find these minimizers with similar accuracy and greater efficiency than techniques using the PDE formulation. These algorithms can be also be used to minimize functionals which do not have an equivalent PDE formulation. We call these algorithms 'Deep Variational Methods' (DVM).en
dc.publisherMontana State University - Bozeman, College of Letters & Scienceen
dc.subject.lcshDifferential equations, Partialen
dc.subject.lcshMachine learningen
dc.subject.lcshFunctional analysisen
dc.titleDVM: a deep learning algorithm for minimizing functionalsen
dc.rights.holderCopyright 2022 by Dominic Robert Bairen, Graduate Committee: Jack D. Dockery; Scott McCallaen Sciences.en

Files in this item


This item appears in the following Collection(s)

Show simple item record

MSU uses DSpace software, copyright © 2002-2017  Duraspace. For library collections that are not accessible, we are committed to providing reasonable accommodations and timely access to users with disabilities. For assistance, please submit an accessibility request for library material.