Multifidelity Cross-validation

TL;DR

This paper introduces a novel multifidelity Gaussian process method with active learning via leave-one-out cross-validation to efficiently emulate high-fidelity models, reducing error and computational cost in engineering applications.

Contribution

It proposes the MFCV approach that adaptively learns correlations across fidelities and optimally selects input-fidelity pairs for improved surrogate modeling accuracy.

Findings

MFCV reduces cross-validation error effectively.

The method outperforms existing approaches on synthetic and real problems.

It improves efficiency in thermal stress analysis of turbine blades.

Abstract

Emulating the mapping between quantities of interest and their control parameters using surrogate models finds widespread application in engineering design, including in numerical optimization and uncertainty quantification. Gaussian process models can serve as a probabilistic surrogate model of unknown functions, thereby making them highly suitable for engineering design and decision-making in the presence of uncertainty. In this work, we are interested in emulating quantities of interest observed from models of a system at multiple fidelities, which trade accuracy for computational efficiency. Using multifidelity Gaussian process models, to efficiently fuse models at multiple fidelities, we propose a novel method to actively learn the surrogate model via leave-one-out cross-validation (LOO-CV). Our proposed multifidelity cross-validation (\texttt{MFCV}) approach develops an adaptive approach to reduce the LOO-CV error at the target (highest) fidelity, by learning the correlations between the LOO-CV at all fidelities. \texttt{MFCV} develops a two-step lookahead policy to select optimal input-fidelity pairs, both in sequence and in batches, both for continuous and discrete fidelity spaces. We demonstrate the utility of our method on several synthetic test problems as well as on the thermal stress analysis of a gas turbine blade.