# Multivariate sensitivity-adaptive polynomial chaos expansion for high-dimensional surrogate modeling and uncertainty quantification

arXiv: https://arxiv.org/abs/2310.09871 · HTML: https://mlsanity.com/paper/2310.09871/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2023.

## Built on by (most cited first, 2 of 2)

- [Conformalized Polynomial Chaos Expansion for Uncertainty-aware Surrogate Modeling](https://mlsanity.com/paper/2510.22375/) (2025)
- [Uncertainty Quantification of Engineering Structures by Polynomial Chaos Expansion and Multivariate Active Learning](https://mlsanity.com/paper/2606.17233/) (2026)

## Abstract (arXiv)

This work develops a novel basis-adaptive method for constructing anisotropic polynomial chaos expansions of multidimensional (vector-valued, multi-output) model responses. The adaptive basis selection is based on multivariate sensitivity analysis metrics that can be estimated by post-processing the polynomial chaos expansion and results in a common anisotropic polynomial basis for the vector-valued response. This allows the application of the method to problems with up to moderately high-dimensional model inputs (in the order of tens) and up to very high-dimensional model responses (in the order of thousands). The method is applied to different engineering test cases for surrogate modeling and uncertainty quantification, including use cases related to electric machine and power grid modeling and simulation, and is found to produce highly accurate results with comparatively low data and computational demand.