Bayesian deep Gaussian processes (DGPs) outperform ordinary GPs as surrogate models of complex computer experiments when response surface dynamics are non-stationary, which is especially prevalent in aerospace simulations. Yet DGP surrogates have not been deployed for the canonical downstream task in that setting: reliability analysis through contour location (CL). Level sets separating passable vs. failable operating conditions are best learned through strategic sequential design. There are two limitations to modern CL methodology which hinder DGP integration in this setting. First, derivative-based optimization underlying acquisition functions is thwarted by sampling-based Bayesian (i.e., MCMC) inference, which is essential for DGP posterior integration. Second, canonical acquisition criteria, such as entropy, are famously myopic to the extent that optimization may even be undesirable. Here we tackle both of these limitations at once, proposing a hybrid criteria that explores along the Pareto front of entropy and (predictive) uncertainty, requiring evaluation only at strategically located "triangulation" candidates. We showcase DGP CL performance in several synthetic benchmark exercises and on a real-world RAE-2822 transonic airfoil simulation.

翻译：贝叶斯深度高斯过程（DGPs）在响应面动力学非平稳时（这在航空航天仿真中尤为常见）作为复杂计算机实验的代理模型，表现优于普通高斯过程。然而，DGP代理模型尚未被应用于该场景下的经典下游任务：通过等值线定位（CL）进行可靠性分析。区分可行与失效运行工况的水平集最好通过战略性序贯设计来学习。现代CL方法存在两个限制，阻碍了DGP在此场景中的集成。首先，基于采样的贝叶斯（即MCMC）推断阻碍了基于导数的采集函数优化，而这对DGP后验积分至关重要。其次，熵等经典采集准则以短视著称，以至于优化可能甚至是不必要的。本文同时解决了这两个限制，提出了一种混合准则，该准则沿熵和（预测）不确定性的帕累托前沿进行探索，仅需在战略性定位的"三角剖分"候选点上进行评估。我们在多个合成基准测试和一个实际RAE-2822跨声速翼型仿真中展示了DGP的CL性能。