Conformalized Polynomial Chaos Expansion for Uncertainty-aware Surrogate Modeling

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, we integrate jackknife-based conformal prediction 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. 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, thus eliminating the need for repeated model re-training. In addition to the efficient computation of the predictive intervals, a significant advantage of this approach is its data efficiency, as it requires no hold-out dataset for prediction interval calibration, thus allowing the entire dataset to be used for model training. The conformalized polynomial chaos expansion method is validated on several benchmark models, where the impact of training data volume on the predictive intervals is additionally investigated.