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 [1]. 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.

[1] Sirignano and Spiliopoulos, "DGM: A deep learning algorithm for solving partial differential equations", Journal of Computational Physics 375 (2018):1339-1364