Bi-fidelity Reduced Polynomial Chaos Expansion for Uncertainty Quantification

TL;DR

This paper introduces a bi-fidelity polynomial chaos expansion method that combines low- and high-fidelity models to efficiently quantify uncertainty in complex engineering systems, reducing computational costs.

Contribution

It develops a stochastic model reduction technique using polynomial chaos, with new error bounds and a practical procedure for model pair assessment.

Findings

The method achieves accuracy comparable to high-fidelity models.

Error bounds effectively guide model pair selection.

Numerical examples demonstrate significant computational savings.

Abstract

A ubiquitous challenge in design space exploration or uncertainty quantification of complex engineering problems is the minimization of computational cost. A useful tool to ease the burden of solving such systems is model reduction. This work considers a stochastic model reduction method (SMR), in the context of polynomial chaos (PC) expansions, where low-fidelity (LF) samples are leveraged to form a stochastic reduced basis. The reduced basis enables the construction of a bi-fidelity (BF) estimate of a quantity of interest from a small number of high-fidelity (HF) samples. A successful BF estimate approximates the quantity of interest with accuracy comparable to the HF model and computational expense close to the LF model. We develop new error bounds for the SMR approach and present a procedure to practically utilize these bounds in order to assess the appropriateness of a given pair of LF and HF models for BF estimation. The effectiveness of the SMR approach, and the utility of the error bound are presented in three numerical examples.