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X-WR-CALDESC:FAU DCN-AvH. Chair for Dynamics, Control, Machine Learning and Numerics -Alexander von Humboldt Professorship
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DTSTART;TZID=Europe/Berlin:20211008T160000
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DTSTAMP:20211020T082746Z
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SUMMARY:On solving/learning differential equations with kernels
DESCRIPTION:Speaker: Prof. Dr. Houman Owhadi\nAffiliation: Caltech (USA)\nOrganized by: FAU DCN-AvH, Chair for Dynamics, Control and Numerics – Alexander von Humboldt Professorship at FAU Erlangen-Nürnberg (Germany)\nZoom meeting link\nMeeting ID: 686 4453 8133 | PIN code: 603054\nAbstract. 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.\nFor 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.\nParts of this talk are joint work with Yifan Chen, Boumediene Hamzi, Bamdad Hosseini, Romit Maulik, Florian Schäfer, Clint Scovel and Andrew Stuart.\nThis event on LinkedIn\n
URL:https://dcn.nat.fau.eu/events/on-solving-learning-differential-equations-with-kernels/
CATEGORIES:FAU DCN-AvH Seminar,Seminar/Talk
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