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Computer simulations have become essential for analyzing complex systems, buthigh-fidelity simulations often come with significant computational costs. Totackle this challenge, multi-fidelity computer experiments have emerged as apromising approach that leverages both low-fidelity and high-fidelitysimulations, enhancing both the accuracy and efficiency of the analysis. Inthis paper, we introduce a new and flexible statistical model, the RecursiveNon-Additive (RNA) emulator, that integrates the data from multi-fidelitycomputer experiments. Unlike conventional multi-fidelity emulation approachesthat rely on an additive auto-regressive structure, the proposed RNA emulatorrecursively captures the relationships between multi-fidelity data usingGaussian process priors without making the additive assumption, allowing themodel to accommodate more complex data patterns. Importantly, we derive theposterior predictive mean and variance of the emulator, which can beefficiently computed in a closed-form manner, leading to significantimprovements in computational efficiency. Additionally, based on this emulator,we introduce three active learning strategies that optimize the balance betweenaccuracy and simulation costs to guide the selection of the fidelity level andinput locations for the next simulation run. We demonstrate the effectivenessof the proposed approach in a suite of synthetic examples and a real-worldproblem. An R package for the proposed methodology is provided in an openrepository.

Active Learning for a Recursive Non-Additive Emulator for Multi-Fidelity Computer Experiments