Deep Learning for PDE: Part II (application to PDE)
Talk by Dr. Dominique Zosso (Dept. of Mathematical Sciences, MSU)
10/15/2020 3:10 pm Webex Meeting
In this unexpectedly separate second part, we focus on a recent approach to use "Deep Galerkin Methods" to numerically tackle (certain) PDE . We construct an ANN to represent the unknown function u: for arbitrary input values x, the network will evaluate to an approximation of u(x), trained using a loss function defined based on the PDE terms. I will illustrate the method (incl. a sketch of its implementation in MATLAB) on a naively-thought-to-be-simple first order PDE problem (linear wave equation) that turns out to be diabolically hard. I will sketch how others have been successful for second order PDE problems.
 Sirignano and Spiliopoulos, "DGM: A deep learning algorithm for solving partial differential equations", Journal of Computational Physics 375 (2018):1339-1364