Date of Award
Master of Science (MS)
Applied Statistics and Data Science
Dr. Hansapani Rodrigo
Dr. Tamer Oraby
Dr. Erwin Suazo
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.
Flores, Stephanie L., "Neural Networks and Stochastic Differential Equations" (2022). Theses and Dissertations. 1272.