Conformalized Polynomial Chaos Expansion for Uncertainty-aware Surrogate Modeling

TL;DR

This paper presents a novel conformalized polynomial chaos expansion method that provides uncertainty quantification through predictive intervals, efficiently leveraging linearity for analytical residual computation, validated on benchmarks and engineering applications.

Contribution

It introduces a conformal prediction approach integrated with polynomial chaos expansions, enabling uncertainty quantification without hold-out data and with analytical residual computation.

Findings

Predictive intervals achieve target coverage even with small datasets.

Training data size significantly improves empirical coverage and interval precision.

Method is validated on benchmark models and engineering design cases.

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.