# Conformalized Polynomial Chaos Expansion for Uncertainty-aware Surrogate Modeling

arXiv: https://arxiv.org/abs/2510.22375 · HTML: https://mlsanity.com/paper/2510.22375/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 62 references that are in the map.
- First posted on arXiv 25 Oct 2025.

## Builds on (most cited first, 26 of 26)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Conformal Prediction: a Unified Review of Theory and New Challenges](https://mlsanity.com/paper/2005.07972/) (2020)
- [Uncertainty Quantification over Graph with Conformalized Graph Neural Networks](https://mlsanity.com/paper/2305.14535/) (2023)
- [Conformal prediction for time series](https://mlsanity.com/paper/2010.09107/) (2020)
- [Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark](https://mlsanity.com/paper/2002.01290/) (2020)
- [Data-driven polynomial chaos expansion for machine learning regression](https://mlsanity.com/paper/1808.03216/) (2018)
- [Polynomial-Chaos-based Kriging](https://mlsanity.com/paper/1502.03939/) (2015)
- [A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems](https://mlsanity.com/paper/2202.04648/) (2022)
- [Physics-constrained polynomial chaos expansion for scientific machine learning and uncertainty quantification](https://mlsanity.com/paper/2402.15115/) (2024)
- [Manifold learning-based polynomial chaos expansions for high-dimensional surrogate models](https://mlsanity.com/paper/2107.09814/) (2021)
- [Physics-Informed Polynomial Chaos Expansions](https://mlsanity.com/paper/2309.01697/) (2023)
- [An active-learning algorithm that combines sparse polynomial chaos expansions and bootstrap for structural reliability analysis](https://mlsanity.com/paper/1709.01589/) (2017)
- [Automatic selection of basis-adaptive sparse polynomial chaos expansions for engineering applications](https://mlsanity.com/paper/2009.04800/) (2020)
- [Uncertainty Quantification of Surrogate Models using Conformal Prediction](https://mlsanity.com/paper/2408.09881/) (2024)
- [Polynomial Chaos Expansion for Operator Learning](https://mlsanity.com/paper/2508.20886/) (2025)
- [Conformalized Physics-Informed Neural Networks](https://mlsanity.com/paper/2405.08111/) (2024)
- [Conformalized Kernel Ridge Regression](https://mlsanity.com/paper/1609.05959/) (2016)
- [Polynomial Chaos Expansions on Principal Geodesic Grassmannian Submanifolds for Surrogate Modeling and Uncertainty Quantification](https://mlsanity.com/paper/2401.16683/) (2024)
- [An hp-adaptive multi-element stochastic collocation method for surrogate modeling with information re-use](https://mlsanity.com/paper/2206.14435/) (2022)
- [Multivariate sensitivity-adaptive polynomial chaos expansion for high-dimensional surrogate modeling and uncertainty quantification](https://mlsanity.com/paper/2310.09871/) (2023)
- [Assessing the Performance of Leja and Clenshaw-Curtis Collocation for Computational Electromagnetics with Random Input Data](https://mlsanity.com/paper/1712.07223/) (2017)
- [Power Module Heat Sink Design Optimization with Ensembles of Data-Driven Polynomial Chaos Surrogate Models](https://mlsanity.com/paper/2205.08746/) (2022)

## Abstract (arXiv)

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.