Conformalized Polynomial Chaos Expansion for Uncertainty-aware Surrogate Modeling

Dimitrios Loukrezis; Dimitris G. Giovanis

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arXiv · 2510.22375

Conformalized Polynomial Chaos Expansion for Uncertainty-aware Surrogate Modeling

Dimitrios Loukrezis·Dimitris G. Giovanis

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Abstract

This work introduces a method to equip data-driven polynomial chaos expansion surrogate models with intervals that quantify the predictive uncertainty of the surrogate. To that end, jackknife-based conformal prediction is integrated into regression-based polynomial chaos expansions. The jackknife algorithm uses leave-one-out residuals to generate predictive intervals around the predictions of the polynomial chaos surrogate. The jackknife+ extension additionally requires leave-one-out model predictions. Both methods allow to use the entire dataset for model training and do not require a hold-out dataset for prediction interval calibration. The key to efficient implementation is to leverage the linearity of the polynomial chaos regression model, so that leave-one-out residuals and, if necessary, leave-one-out model predictions can be computed with analytical, closed-form expressions. This eliminates the need for repeated model re-training. The conformalized polynomial chaos expansion method is first validated on four benchmark models and then applied to two electrical engineering design use-cases. The method produces predictive intervals that provide the target coverages, even for low-accuracy models trained with small datasets. At the same time, training data availability plays a crucial role in improving the empirical coverage and narrowing the predictive interval, as well as in reducing their variability over different training datasets.

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BibTeX RIS

Dimitrios Loukrezis, Dimitris G. Giovanis. 2025-12-17. Conformalized Polynomial Chaos Expansion for Uncertainty-aware Surrogate Modeling. https://arxiv.org/abs/2510.22375

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