  Computer simulations have become essential for analyzing complex systems, but
high-fidelity simulations often come with significant computational costs. To
tackle this challenge, multi-fidelity computer experiments have emerged as a
promising approach that leverages both low-fidelity and high-fidelity
simulations, enhancing both the accuracy and efficiency of the analysis. In
this paper, we introduce a new and flexible statistical model, the Recursive
Non-Additive (RNA) emulator, that integrates the data from multi-fidelity
computer experiments. Unlike conventional multi-fidelity emulation approaches
that rely on an additive auto-regressive structure, the proposed RNA emulator
recursively captures the relationships between multi-fidelity data using
Gaussian process priors without making the additive assumption, allowing the
model to accommodate more complex data patterns. Importantly, we derive the
posterior predictive mean and variance of the emulator, which can be
efficiently computed in a closed-form manner, leading to significant
improvements in computational efficiency. Additionally, based on this emulator,
we introduce four active learning strategies that optimize the balance between
accuracy and simulation costs to guide the selection of the fidelity level and
input locations for the next simulation run. We demonstrate the effectiveness
of the proposed approach in a suite of synthetic examples and a real-world
problem. An R package RNAmf for the proposed methodology is provided on CRAN.
