One of the main challenges in surrogate modeling is the limited availability of data due to resource constraints associated with computationally expensive simulations. Multi-fidelity methods provide a solution by chaining models in a hierarchy with increasing fidelity, associated with lower error, but increasing cost. In this paper, we compare different multi-fidelity methods employed in constructing Gaussian process surrogates for regression. Non-linear autoregressive methods in the existing literature are primarily confined to two-fidelity models, and we extend these methods to handle more than two levels of fidelity. Additionally, we propose enhancements for an existing method incorporating delay terms by introducing a structured kernel. We demonstrate the performance of these methods across various academic and real-world scenarios. Our findings reveal that multi-fidelity methods generally have a smaller prediction error for the same computational cost as compared to the single-fidelity method, although their effectiveness varies across different scenarios.

翻译：代理建模面临的主要挑战之一是，由于计算资源有限导致的高成本仿真数据获取困难。多保真度方法通过将模型按保真度等级（对应更低误差但更高成本）进行层级串联来提供解决方案。本文比较了构建高斯过程回归代理时使用的多种多保真度方法。现有文献中的非线性自回归方法主要局限于双保真度模型，我们将其扩展至支持两个以上保真度等级。此外，我们通过引入结构化核函数，对一种包含延时项的现有方法提出改进。我们在多种学术与真实场景中验证了这些方法的性能。结果表明，相较于单保真度方法，多保真度方法在相同计算成本下通常具有更低的预测误差，但其有效性因场景而异。