Conformalized polynomial chaos expansion for uncertainty‐aware surrogate modeling

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 prediction intervals around the predictions of the polynomial chaos surrogate. The jackknife+ extension additionally requires leave‐one‐out model predictions. Both methods allow using 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 benchmark models and then applied to an engineering use case. The method produces prediction 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 prediction interval, as well as in reducing their variability over different training datasets.