Proofs and algorithms seminar: Ander Gray on Wednesday 02 April 2025 at 13h30, "Guaranteed confidence-bands for PDE surrogates"

===== Seminar of the proofs and algorithms pole =====

Hello everybody,

For a new seminar of the proofs and algorithms pole of LIX, we are happy to welcome Ander Gray (Heudiasyc, Université de Technologie de Compiègne), invited by the COSYNUS team.

***** Wednesday 02 April 2025 at 13h30, room Grace Hopper *****

Ander Gray -- Guaranteed confidence-bands for PDE surrogates

I present a method for computing statistically guaranteed confidence bands for functional surrogate modes: surrogate models which map between function spaces, motivated by the need build reliable physics emulators. The method constructs nested confidence sets on a low-dimensional representation (an SVD) of the surrogate model’s prediction error, and then maps these sets to the prediction space using set-propagation techniques. The result is conformal-like coverage guaranteed prediction sets for functional 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: [arXiv.2501.18426](https://doi.org/10.48550/arXiv.2501.18426)


The following seminar will be on Friday 11 April 2025 at 14h00 by Sam van Gool.

The list of upcoming seminars can be found at:
https://www.lix.polytechnique.fr/proofs-algorithms/seminar/

The calendar of seminars can be found at:
https://www.lix.polytechnique.fr/proofs-algorithms/seminar/calendar.ics

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