# Automatic selection of basis-adaptive sparse polynomial chaos expansions for engineering applications

arXiv: https://arxiv.org/abs/2009.04800 · HTML: https://mlsanity.com/paper/2009.04800/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Sep 2020.

## Built on by (most cited first, 11 of 11)

- [Physics-Informed Polynomial Chaos Expansions](https://mlsanity.com/paper/2309.01697/) (2023)
- [On efficient algorithms for computing near-best polynomial approximations to high-dimensional, Hilbert-valued functions from limited samples](https://mlsanity.com/paper/2203.13908/) (2022)
- [Polynomial Chaos Expansions on Principal Geodesic Grassmannian Submanifolds for Surrogate Modeling and Uncertainty Quantification](https://mlsanity.com/paper/2401.16683/) (2024)
- [Deep Polynomial Chaos Expansion](https://mlsanity.com/paper/2507.21273/) (2025)
- [Uncertainty-aware multi-fidelity surrogate modeling with noisy data](https://mlsanity.com/paper/2401.06447/) (2024)
- [Bayesian full waveform inversion with sequential surrogate model refinement](https://mlsanity.com/paper/2505.03246/) (2025)
- [AL-SPCE - Reliability analysis for nondeterministic models using stochastic polynomial chaos expansions and active learning](https://mlsanity.com/paper/2507.04553/) (2025)
- [Surrogate modeling for uncertainty quantification in nonlinear dynamics](https://mlsanity.com/paper/2507.12358/) (2025)
- [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)
- [Conformalized Polynomial Chaos Expansion for Uncertainty-aware Surrogate Modeling](https://mlsanity.com/paper/2510.22375/) (2025)

## Abstract (arXiv)

Sparse polynomial chaos expansions (PCE) are an efficient and widely used surrogate modeling method in uncertainty quantification for engineering problems with computationally expensive models. To make use of the available information in the most efficient way, several approaches for so-called basis-adaptive sparse PCE have been proposed to determine the set of polynomial regressors ("basis") for PCE adaptively. The goal of this paper is to help practitioners identify the most suitable methods for constructing a surrogate PCE for their model. We describe three state-of-the-art basis-adaptive approaches from the recent sparse PCE literature and conduct an extensive benchmark in terms of global approximation accuracy on a large set of computational models. Investigating the synergies between sparse regression solvers and basis adaptivity schemes, we find that the choice of the proper solver and basis-adaptive scheme is very important, as it can result in more than one order of magnitude difference in performance. No single method significantly outperforms the others, but dividing the analysis into classes (regarding input dimension and experimental design size), we are able to identify specific sparse solver and basis adaptivity combinations for each class that show comparatively good performance. To further improve on these findings, we introduce a novel solver and basis adaptivity selection scheme guided by cross-validation error. We demonstrate that this automatic selection procedure provides close-to-optimal results in terms of accuracy, and significantly more robust solutions, while being more general than the case-by-case recommendations obtained by the benchmark.