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). In that context, we are motivated by a simulation of an RAE-2822 transonic airfoil which demarcates efficient and inefficient flight conditions. Level sets separating passable versus 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 criterion 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 the RAE-2822 airfoil.

翻译：贝叶斯深度高斯过程(DGPs)作为复杂计算机实验的替代模型，在响应面动态呈现非平稳特性时（这在航空航天仿真中尤为常见），其性能优于普通高斯过程。然而，DGP代理模型尚未被应用于该领域的关键下游任务：通过轮廓定位(CL)实现可靠性分析。在此背景下，我们受RAE-2822跨声速翼型仿真启发——该仿真可区分高效与低效飞行工况。分离可通过与不可通过运行工况的等值线，最好通过策略性序贯设计来学习。现代CL方法存在两个限制DGP在此场景中整合的瓶颈：首先，基于采样的贝叶斯（即MCMC）推断阻碍了采集函数所依赖的导数优化，而这对DGP后验积分至关重要；其次，熵等经典采集准则存在著名的短视性，以至于优化本身可能不可取。我们在此同时解决这两个限制，提出一种混合准则：沿熵与（预测）不确定性构成的Pareto前沿进行探索，仅需在策略性定位的"三角剖分"候选点进行评估。我们通过若干合成基准测试及RAE-2822翼型案例，展示了DGP轮廓定位的性能表现。