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SUMMARY:Guaranteed confidence-bands for PDE surrogates - Ander Gray (Unive
 rsité de Technologie de Compiègne)
DTSTART:20250606T085000Z
DTEND:20250606T091000Z
UID:TALK230830@talks.cam.ac.uk
DESCRIPTION:\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nCo-aut
 hors: Vignesh Gopakumar\, Sylvain Rousseau\, Sebastien Destercke&nbsp\;\n&
 nbsp\;\nWe present a method for computing statistically guaranteed confide
 nce bands for functional surrogate modes: surrogate models which map betwe
 en function spaces\, motivated by the need build reliable physics emulator
 s. The method constructs nested confidence sets on a low-dimensional repre
 sentation (an SVD) of the surrogate model's prediction error\, and then ma
 ps these sets to the prediction space using set-propagation techniques. Th
 e result is conformal-like coverage guaranteed prediction sets for functio
 nal surrogate models. We use zonotopes as basis of the set construction\, 
 due to their well-studied set-propagation and verification properties. The
  method is model agnostic and can thus be applied to complex Sci-ML models
 \, including Neural Operators\, but also in simpler settings. An important
  step is a technique to capture the truncation error of the SVD\, ensuring
  the guarantees of the method. A preprint is available here: https://doi.o
 rg/10.48550/arXiv.2501.18426\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
 \n\n\n\n\n
LOCATION:Seminar Room 1\, Newton Institute
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