Modern scientific problems are often multi-disciplinary and require integration of computer models from different disciplines, each with distinct functional complexities, programming environments, and computation times. Linked Gaussian process (LGP) emulation tackles this challenge through a divide-and-conquer strategy that integrates Gaussian process emulators of the individual computer models in a network. However, the required stationarity of the component Gaussian process emulators within the LGP framework limits its applicability in many real-world applications. In this work, we conceptualize a network of computer models as a deep Gaussian process with partial exposure of its hidden layers. We develop a method for inference for these partially exposed deep networks that retains a key strength of the LGP framework, whereby each model can be emulated separately using a DGP and then linked together. We show in both synthetic and empirical examples that our linked deep Gaussian process emulators exhibit significantly better predictive performance than standard LGP emulators in terms of accuracy and uncertainty quantification. They also outperform single DGPs fitted to the network as a whole because they are able to integrate information from the partially exposed hidden layers. Our methods are implemented in an R package $\texttt{dgpsi}$ that is freely available on CRAN.

翻译：现代科学问题通常具有多学科性，需要整合来自不同学科的计算机模型，这些模型在功能复杂性、编程环境和计算时间上存在显著差异。链接高斯过程（LGP）仿真通过分治策略应对这一挑战，将网络中各个计算机模型的高斯过程仿真器进行集成。然而，LGP框架中组件高斯过程仿真器所需的平稳性限制了其在许多实际应用中的适用性。在本研究中，我们将计算机模型网络概念化为一个具有部分暴露隐藏层的深度高斯过程。我们开发了一种针对这些部分暴露深度网络的推理方法，该方法保留了LGP框架的关键优势，即每个模型可单独使用DGP进行仿真后再链接。通过合成与实证案例，我们证明了链接深度高斯过程仿真器在预测精度和不确定性量化方面显著优于标准LGP仿真器。此外，由于能够整合部分暴露隐藏层的信息，它们也优于对整个网络拟合的单一DGP。我们的方法已在R包$\texttt{dgpsi}$中实现，并可于CRAN免费获取。