Computer models are used as a way to explore complex physical systems. Stationary Gaussian process emulators, with their accompanying uncertainty quantification, are popular surrogates for computer models. However, many computer models are not well represented by stationary Gaussian processes models. Deep Gaussian processes have been shown to be capable of capturing non-stationary behaviors and abrupt regime changes in the computer model response. In this paper, we explore the properties of two deep Gaussian process formulations within the context of computer model emulation. For one of these formulations, we introduce a new parameter that controls the amount of smoothness in the deep Gaussian process layers. We adapt a stochastic variational approach to inference for this model, allowing for prior specification and posterior exploration of the smoothness of the response surface. Our approach can be applied to a large class of computer models, and scales to arbitrarily large simulation designs. The proposed methodology was motivated by the need to emulate an astrophysical model of the formation of binary black hole mergers.

翻译：计算机模型被用作探索复杂物理系统的一种手段。具有伴随不确定性量化的平稳高斯过程仿真器是计算机模型的常用替代模型。然而，许多计算机模型无法通过平稳高斯过程模型得到良好表征。深度高斯过程已被证明能够捕捉计算机模型响应中的非平稳行为和突变状态转换。本文在计算机模型仿真的背景下，探讨了两种深度高斯过程公式的特性。针对其中一种公式，我们引入了一个控制深度高斯过程层平滑程度的新参数。我们为该模型采用了一种随机变分推理方法，实现了对响应曲面平滑度的先验设定和后验探索。该方法可应用于广泛的计算机模型类别，并能扩展至任意大规模仿真设计。本研究所提出的方法源于对双黑洞并合形成天体物理模型进行仿真的实际需求。