Multifidelity uncertainty quantification with models based on dissimilar parameters

TL;DR

This paper introduces a novel multifidelity uncertainty quantification method that uses a shared manifold to improve correlation among models with different parameters, enhancing estimator efficiency.

Contribution

It proposes a new sampling strategy leveraging the adaptive basis method to transform models onto a shared low-dimensional manifold, addressing correlation issues in dissimilar parameter models.

Findings

Improved correlation among dissimilar models using the shared manifold approach.

Enhanced variance reduction in uncertainty estimates across multiple examples.

Effective for both legacy and non-legacy high-fidelity data scenarios.

Abstract

Multifidelity uncertainty quantification (MF UQ) sampling approaches have been shown to significantly reduce the variance of statistical estimators while preserving the bias of the highest-fidelity model, provided that the low-fidelity models are well correlated. However, maintaining a high level of correlation can be challenging, especially when models depend on different input uncertain parameters, which drastically reduces the correlation. Existing MF UQ approaches do not adequately address this issue. In this work, we propose a new sampling strategy that exploits a shared space to improve the correlation among models with dissimilar parametrization. We achieve this by transforming the original coordinates onto an auxiliary manifold using the adaptive basis (AB) method~\cite{Tipireddy2014}. The AB method has two main benefits: (1) it provides an effective tool to identify the low-dimensional manifold on which each model can be represented, and (2) it enables easy transformation of polynomial chaos representations from high- to low-dimensional spaces. This latter feature is used to identify a shared manifold among models without requiring additional evaluations. We present two algorithmic flavors of the new estimator to cover different analysis scenarios, including those with legacy and non-legacy high-fidelity data. We provide numerical results for analytical examples, a direct field acoustic test, and a finite element model of a nuclear fuel assembly. For all examples, we compare the proposed strategy against both single-fidelity and MF estimators based on the original model parametrization.