Multifidelity cross-validation

Ashwin Renganathan

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 (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. 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.