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SUMMARY:Houman Owhadi (California Institute of Technology\, USA)
DTSTART:20210921T140000Z
DTEND:20210921T150000Z
DTSTAMP:20260423T052326Z
UID:SNAP/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SNAP/10/">On
  solving/learning differential equations with kernels</a>\nby Houman Owhad
 i (California Institute of Technology\, USA) as part of Seminars on Numeri
 cs and Applications\n\n\nAbstract\nWe present a simple\, rigorous\, and un
 ified framework for solving and learning (possibly nonlinear) differential
  equations (PDEs and ODEs) using the framework of Gaussian processes/kerne
 l methods.\nFor PDEs the proposed approach:<br />\n(1) provides a natural 
 generalization of collocation kernel methods to nonlinear PDEs and Inverse
  Problems\;<br />\n(2) has guaranteed convergence for a very general class
  of PDEs\, and comes equipped with a path to compute error bounds for spec
 ific PDE approximations\;<br />\n(3) inherits the state-of-the-art computa
 tional complexity of linear solvers for dense kernel matrices.<br />\nFor 
 ODEs\, we illustrate the efficacy of the proposed approach by extrapolatin
 g weather/climate time series obtained from satellite data and illustrate 
 the importance of using adapted/learned kernels.<br />\n<i>Parts of this t
 alk are joint work with Yifan Chen\, Boumediene Hamzi\, Bamdad Hosseini\, 
 Romit Maulik\, Florian Schäfer\, Clint Scovel and Andrew Stuart.</i>\n
LOCATION:https://researchseminars.org/talk/SNAP/10/
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