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 three 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 for the proposed methodology is provided in an open repository.

翻译：计算机模拟已成为分析复杂系统的关键工具，但高保真模拟往往伴随显著的计算成本。为应对这一挑战，多保真计算机实验作为一种新兴方法，通过整合低保真与高保真模拟数据，既能提升分析精度，又能提高计算效率。本文提出一种灵活的新型统计模型——递归非加性仿真器，用于融合多保真计算机实验数据。与依赖加性自回归结构的传统多保真仿真方法不同，该仿真器基于高斯过程先验递归捕获多保真数据间的关系，无需加性假设，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，我们提出了三种主动学习策略，在精度与模拟成本之间实现最优平衡，以指导下一次模拟运行的保真度层级与输入位置选择。我们通过一系列合成实例及一个实际问题验证了该方法的有效性。相关R语言开源包已在公共存储库中提供。