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成本高昂的模拟所导致的资源限制，使得可用数据有限。多保真度方法通过将模型按保真度递增（误差降低但成本增加）的层次结构进行链式组合，为此提供了解决方案。本文比较了用于构建高斯过程回归代理模型的不同多保真度方法。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，我们将这些方法扩展至处理超过两个保真度层级的情况。此外，我们通过引入结构化核函数，对现有包含延迟项的方法提出了改进方案。我们在多种学术场景和实际场景中验证了这些方法的性能。研究结果表明，在相同计算成本下，多保真度方法通常比单保真度方法具有更小的预测误差，但其有效性在不同场景中有所差异。