  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.
