Guaranteed confidence-bands for PDE surrogates

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• Ander Gray (Université de Technologie de Compiègne)
• Friday 06 June 2025, 09:50-10:10
• Seminar Room 1, Newton Institute.

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RCLW02 - Calibrating prediction uncertainty : statistics and machine learning perspectives

Co-authors: Vignesh Gopakumar, Sylvain Rousseau, Sebastien Destercke    We 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: https://doi.org/10.48550/arXiv.2501.18426

This talk is part of the Isaac Newton Institute Seminar Series series.

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