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.

翻译：计算机模拟已成为分析复杂系统的重要手段，但高保真度模拟通常伴随着巨大的计算成本。为应对这一挑战，多保真度计算机实验作为一种有前景的方法应运而生，它同时利用低保真度和高保真度模拟，从而提升分析的准确性与效率。本文提出一种新颖且灵活的统计模型——递归非加性（RNA）仿真器，该模型能够整合多保真度计算机实验的数据。与依赖加性自回归结构的传统多保真度仿真方法不同，所提出的RNA仿真器通过高斯过程先验递归地捕捉多保真度数据间的关系，无需依赖加性假设，从而能够适应更复杂的数据模式。重要的是，我们推导了该仿真器的后验预测均值与方差，这些量可通过闭式形式高效计算，显著提升了计算效率。此外，基于该仿真器，我们提出了四种主动学习策略，以优化精度与模拟成本间的平衡，从而指导下一轮模拟实验中保真度水平与输入位置的选取。我们通过一系列合成算例和一个实际案例验证了所提方法的有效性。相关方法的R软件包RNAmf已在CRAN平台发布。