Deep learning for PDE: part II (application to PDE)
- Thursday, October 15, 2020 from 3:00pm to 4:00pm
- Webex Meeting number: 120 556 7048 Password: applied
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.
- Department of Mathematical Sciences