Adaptive Multi-index Collocation for Uncertainty Quantification and Sensitivity Analysis

TL;DR

This paper introduces an adaptive multi-index stochastic collocation algorithm that efficiently constructs response surface surrogates for high-fidelity models, enabling accurate uncertainty quantification and sensitivity analysis at reduced computational costs.

Contribution

It proposes a novel adaptive algorithm that balances errors from physical discretization and response surface approximation using multi-index stochastic collocation.

Findings

Achieves over two orders of magnitude more accuracy than single fidelity methods.

Effective on complex multi-physics models and canonical UQ test problems.

Reduces computational cost for high-accuracy uncertainty analysis.

Abstract

In this paper, we present an adaptive algorithm to construct response surface approximations of high-fidelity models using a hierarchy of lower fidelity models. Our algorithm is based on multi-index stochastic collocation and automatically balances physical discretization error and response surface error to construct an approximation of model outputs. This surrogate can be used for uncertainty quantification (UQ) and sensitivity analysis (SA) at a fraction of the cost of a purely high-fidelity approach. We demonstrate the effectiveness of our algorithm on a canonical test problem from the UQ literature and a complex multi-physics model that simulates the performance of an integrated nozzle for an unmanned aerospace vehicle. We find that, when the input-output response is sufficiently smooth, our algorithm produces approximations that can be over two orders of magnitude more accurate than single fidelity approximations for a fixed computational budget.