# Data-driven polynomial chaos expansion for machine learning regression

arXiv: https://arxiv.org/abs/1808.03216 · HTML: https://mlsanity.com/paper/1808.03216/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Aug 2018.

## Built on by (most cited first, 25 of 25)

- [Uncertainty Quantification in Machine Learning for Engineering Design and Health Prognostics: A Tutorial](https://mlsanity.com/paper/2305.04933/) (2023)
- [Generalised Latent Assimilation in Heterogeneous Reduced Spaces with Machine Learning Surrogate Models](https://mlsanity.com/paper/2204.03497/) (2022)
- [Neural Chaos: A Spectral Stochastic Neural Operator](https://mlsanity.com/paper/2502.11835/) (2025)
- [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)
- [Physics-Informed Polynomial Chaos Expansions](https://mlsanity.com/paper/2309.01697/) (2023)
- [Polynomial Chaos Expansion for Operator Learning](https://mlsanity.com/paper/2508.20886/) (2025)
- [PCENet: High Dimensional Surrogate Modeling for Learning Uncertainty](https://mlsanity.com/paper/2202.05063/) (2022)
- [On Fractional Moment Estimation from Polynomial Chaos Expansion](https://mlsanity.com/paper/2403.01948/) (2024)
- [Deep Polynomial Chaos Expansion](https://mlsanity.com/paper/2507.21273/) (2025)
- [Capturing and incorporating expert knowledge into machine learning models for quality prediction in manufacturing](https://mlsanity.com/paper/2202.02003/) (2022)
- [Polynomial Chaos Surrogate Construction for Random Fields with Parametric Uncertainty](https://mlsanity.com/paper/2311.00553/) (2023)
- [Rare event estimation using stochastic spectral embedding](https://mlsanity.com/paper/2106.05824/) (2021)
- [Bayesian tomography using polynomial chaos expansion and deep generative networks](https://mlsanity.com/paper/2307.04228/) (2023)
- [Wiener Chaos in Kernel Regression: Towards Untangling Aleatoric and Epistemic Uncertainty](https://mlsanity.com/paper/2312.07387/) (2023)
- [Uncertainty-aware multi-fidelity surrogate modeling with noisy data](https://mlsanity.com/paper/2401.06447/) (2024)
- [Polynomial Chaos Expanded Gaussian Process](https://mlsanity.com/paper/2405.01052/) (2024)
- [Gradient-enhanced global sensitivity analysis with Poincar'e chaos expansions](https://mlsanity.com/paper/2510.03056/) (2025)
- [Conformal prediction for full and sparse polynomial chaos expansions](https://mlsanity.com/paper/2601.16636/) (2026)
- [Data-driven sparse polynomial chaos expansion for models with dependent inputs](https://mlsanity.com/paper/2101.07997/) (2021)
- [Surrogate-based variational data assimilation for tidal modelling](https://mlsanity.com/paper/2106.11926/) (2021)
- [A Resolution Independent Neural Operator](https://mlsanity.com/paper/2407.13010/) (2024)
- [Bayesian Surrogate Training on Multiple Data Sources: A Hybrid Modeling Strategy](https://mlsanity.com/paper/2412.11875/) (2024)
- [MF-GLaM: A multifidelity stochastic emulator using generalized lambda models](https://mlsanity.com/paper/2507.10303/) (2025)
- [Conformalized Polynomial Chaos Expansion for Uncertainty-aware Surrogate Modeling](https://mlsanity.com/paper/2510.22375/) (2025)

## Abstract (arXiv)

We present a regression technique for data-driven problems based on polynomial chaos expansion (PCE). PCE is a popular technique in the field of uncertainty quantification (UQ), where it is typically used to replace a runnable but expensive computational model subject to random inputs with an inexpensive-to-evaluate polynomial function. The metamodel obtained enables a reliable estimation of the statistics of the output, provided that a suitable probabilistic model of the input is available. Machine learning (ML) regression is a research field that focuses on providing purely data-driven input-output maps, with the focus on pointwise prediction accuracy. We show that a PCE metamodel purely trained on data can yield pointwise predictions whose accuracy is comparable to that of other ML regression models, such as neural networks and support vector machines. The comparisons are performed on benchmark datasets available from the literature. The methodology also enables the quantification of the output uncertainties, and is robust to noise. Furthermore, it enjoys additional desirable properties, such as good performance for small training sets and simplicity of construction, with only little parameter tuning required.