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SUMMARY:Physics informed Gaussian process priors - Iain Henderson (ISAE-Su
 paéro)
DTSTART:20250827T100000Z
DTEND:20250827T103000Z
UID:TALK234490@talks.cam.ac.uk
DESCRIPTION:Given a linear partial differential equation (PDE)\, I will di
 scuss the design of Gaussian process (GP) priors for the approximation of 
 its solutions as well as its physical parameters. As standard PDE theory i
 s based on weak or distributional formulations\, I will describe necessary
  and sufficient conditions on the kernel of a centered GP so that its real
 isations solve the PDE almost surely\, in the distributional sense. I will
  then describe necessary and sufficient conditions so that the samples of 
 a centered GP lie in a given Sobolev space\, as the latter are particularl
 y well-suited for the study of PDEs. Importantly\, both results do not mak
 e any continuity assumptions on the GP model\, as PDE theory shows that su
 ch assumptions are sometimes too restrictive. If time permits\, I will des
 cribe an application of such GP models for the approximation of the initia
 l data of the 3D wave equation\, as is e.g. the goal of photo-acoustic tom
 ography.
LOCATION:Seminar Room 1\, Newton Institute
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