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

TL;DR

This paper introduces a basis-adaptive polynomial chaos expansion method that leverages multivariate sensitivity analysis to efficiently build surrogate models for high-dimensional, multi-output systems, significantly reducing computational costs.

Contribution

It presents a novel basis-adaptive approach for anisotropic polynomial chaos expansions using sensitivity metrics, enabling effective modeling of high-dimensional responses.

Findings

Achieves high accuracy with low data requirements.

Applicable to problems with high-dimensional inputs and outputs.

Demonstrates effectiveness on engineering test cases.

Abstract

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.