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Virtual LANS Seminar
June 9, 2021 @ 10:30 - 11:30 CDT
Seminar Title: Solving PDEs With Gaussian Processes
Speaker: Andrew Stuart
Title: Bren Professor of Computing and Mathematical Sciences, Caltech
Date/Time: June 9, 2021 / 10:30 AM – 11:30 AM
Location: See meeting URL on the cels-seminars website (requires Argonne login)
Description: We describe an approach to solving PDEs in which the solution is found by minimizing a squared RKHS norm subject to a penalty, or constraint, defined via the PDE. This links to the subject of Gaussian processes subject to pointwise nonlinear constraints. We introduce a framework for the methodology, establish convergence of the resulting numerical method, and describe numerical results. Forward problems for a nonlinear elliptic PDE, Burgers’ equation and a regularized Eikonal equation are presented; and the method is extended to inverse problems and applied to the problem of permeability identification in the Darcy model of flow in a porous medium.
This is in collaboration with Yifan Chen, Bamdad Hosseini and Houman Owhadi.
Please note that the meeting URL for this event can be seen on the cels-seminars website, which requires an Argonne login.