Guaranteed Prediction Sets for Functional Surrogate Models

Ander Gray, Vignesh Gopakumar, Sylvain Rousseau, Sebastien Destercke
Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, PMLR 286:1569-1585, 2025.

Abstract

We propose a method for obtaining statistically guaranteed prediction sets for functional machine learning methods: surrogate models which map between function spaces, motivated by the need to build reliable PDE emulators. The method constructs nested prediction sets on a low-dimensional representation (an SVD) of the surrogate model’s error, and then maps these sets to the prediction space using set-propagation techniques. This results in prediction sets for functional surrogate models with conformal prediction coverage guarantees. We use zonotopes as basis of the set construction, which allow an exact linear propagation and are closed under Cartesian products, making them well-suited to this high-dimensional problem. The method is model agnostic and can thus be applied to complex Sci-ML models, including Neural Operators, but also in simpler settings. We also introduce a technique to capture the truncation error of the SVD, preserving the guarantees of the method.

Cite this Paper

BibTeX
@InProceedings{pmlr-v286-gray25a, title = {Guaranteed Prediction Sets for Functional Surrogate Models}, author = {Gray, Ander and Gopakumar, Vignesh and Rousseau, Sylvain and Destercke, Sebastien}, booktitle = {Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence}, pages = {1569--1585}, year = {2025}, editor = {Chiappa, Silvia and Magliacane, Sara}, volume = {286}, series = {Proceedings of Machine Learning Research}, month = {21--25 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v286/main/assets/gray25a/gray25a.pdf}, url = {https://proceedings.mlr.press/v286/gray25a.html}, abstract = {We propose a method for obtaining statistically guaranteed prediction sets for functional machine learning methods: surrogate models which map between function spaces, motivated by the need to build reliable PDE emulators. The method constructs nested prediction sets on a low-dimensional representation (an SVD) of the surrogate model’s error, and then maps these sets to the prediction space using set-propagation techniques. This results in prediction sets for functional surrogate models with conformal prediction coverage guarantees. We use zonotopes as basis of the set construction, which allow an exact linear propagation and are closed under Cartesian products, making them well-suited to this high-dimensional problem. The method is model agnostic and can thus be applied to complex Sci-ML models, including Neural Operators, but also in simpler settings. We also introduce a technique to capture the truncation error of the SVD, preserving the guarantees of the method.} }
Endnote
%0 Conference Paper %T Guaranteed Prediction Sets for Functional Surrogate Models %A Ander Gray %A Vignesh Gopakumar %A Sylvain Rousseau %A Sebastien Destercke %B Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2025 %E Silvia Chiappa %E Sara Magliacane %F pmlr-v286-gray25a %I PMLR %P 1569--1585 %U https://proceedings.mlr.press/v286/gray25a.html %V 286 %X We propose a method for obtaining statistically guaranteed prediction sets for functional machine learning methods: surrogate models which map between function spaces, motivated by the need to build reliable PDE emulators. The method constructs nested prediction sets on a low-dimensional representation (an SVD) of the surrogate model’s error, and then maps these sets to the prediction space using set-propagation techniques. This results in prediction sets for functional surrogate models with conformal prediction coverage guarantees. We use zonotopes as basis of the set construction, which allow an exact linear propagation and are closed under Cartesian products, making them well-suited to this high-dimensional problem. The method is model agnostic and can thus be applied to complex Sci-ML models, including Neural Operators, but also in simpler settings. We also introduce a technique to capture the truncation error of the SVD, preserving the guarantees of the method.
APA
Gray, A., Gopakumar, V., Rousseau, S. & Destercke, S.. (2025). Guaranteed Prediction Sets for Functional Surrogate Models. Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 286:1569-1585 Available from https://proceedings.mlr.press/v286/gray25a.html.

Related Material