On solving/learning differential equations with kernels

Speaker: Prof. Dr. Houman Owhadi
Affiliation: Caltech (USA)
Organized by: FAU DCN-AvH, Chair for Dynamics, Control and Numerics – Alexander von Humboldt Professorship at FAU Erlangen-Nürnberg (Germany)

Zoom meeting link
Meeting ID: 686 4453 8133 | PIN code: 603054

Abstract. We present a simple, rigorous, and unified framework for solving and learning (possibly nonlinear) differential equations (PDEs and ODEs) using the framework of Gaussian processes/kernel methods.

For PDEs the proposed approach: (1) provides a natural generalization of collocation kernel methods to nonlinear PDEs and Inverse Problems; (2) has guaranteed convergence for a very general class of PDEs, and comes equipped with a path to compute error bounds for specific PDE approximations; (3) inherits the state-of-the-art computational complexity of linear solvers for dense kernel matrices. For ODEs, we illustrate the efficacy of the proposed approach by extrapolating weather/climate time series obtained from satellite data and highlight the importance of using adapted/learned kernels.

Parts of this talk are joint work with Yifan Chen, Boumediene Hamzi, Bamdad Hosseini, Romit Maulik, Florian Schäfer, Clint Scovel and Andrew Stuart.

This event on LinkedIn

The event is finished.

No Responses

© 2019-2022 FAU DCN-AvH Chair for Dynamics, Control and Numerics - Alexander von Humboldt Professorship at Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany | Imprint | Contact