Neural Networks and Stochastic Differential Equations

Author

Stephanie L. Flores, The University of Texas Rio Grande Valley

Date of Award

8-2022

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Applied Statistics and Data Science

First Advisor

Dr. Hansapani Rodrigo

Second Advisor

Dr. Tamer Oraby

Third Advisor

Dr. Erwin Suazo

Abstract

Influenced by the seminal work, “Physics Informed Neural Networks” by Raissi et al., 2017, there has been a growing interest in solving and parameter estimation of Nonlinear Partial Differential Equations (PDE) with Deep Neural networks in recent years. In fact, this has broadened the pathways and shed light on deep learning of stochastic differential equations (SDE) and stochastic PDE’s (SPDE).In this work, we intend to investigate the current approaches of solving and parameter estimation of the SDE/SPDE with deep neural networks and the possibility of extending them to obtain more accurate/stable solutions with residual systems and/or generative adversarial neural networks. We will also apply these methods to study real-world applications of SDE/SPDE problems. The combination of methods can improve speeds, accuracy, and lessen data-related difficulties in solving Stochastic PDEs. Such improvements can assist a wide array of the sciences in computational research and data sciences.

Comments

Copyright 2022 Stephanie L. Flores. All Rights Reserved.

https://go.openathens.net/redirector/utrgv.edu?url=https://www.proquest.com/dissertations-theses/neural-networks-stochastic-differential-equations/docview/2748416538/se-2?accountid=7119

Recommended Citation

Flores, Stephanie L., "Neural Networks and Stochastic Differential Equations" (2022). Theses and Dissertations. 1272.
https://scholarworks.utrgv.edu/etd/1272