Surrogate models are statistical or conceptual approximations for more complex simulation models. In this context, it is crucial to propagate the uncertainty induced by limited simulation budget and surrogate approximation error to predictions, inference, and subsequent decision-relevant quantities. However, quantifying and then propagating the uncertainty of surrogates is usually limited to special analytic cases or is otherwise computationally very expensive. In this paper, we propose a framework enabling a scalable, Bayesian approach to surrogate modeling with thorough uncertainty quantification, propagation, and validation. Specifically, we present three methods for Bayesian inference with surrogate models given measurement data. This is a task where the propagation of surrogate uncertainty is especially relevant, because failing to account for it may lead to biased and/or overconfident estimates of the parameters of interest. We showcase our approach in three detailed case studies for linear and nonlinear real-world modeling scenarios. Uncertainty propagation in surrogate models enables more reliable and safe approximation of expensive simulators and will therefore be useful in various fields of applications.

翻译：代理模型是用于替代更复杂仿真模型的统计或概念近似。在此背景下，将有限仿真预算和代理近似误差所引发的不确定性传播至预测、推断及后续决策相关量至关重要。然而，量化并进而传播代理模型的不确定性通常仅限于特殊的解析情形，否则计算成本极高。本文提出一个框架，支持采用可扩展的贝叶斯方法进行代理建模，并实现全面的不确定性量化、传播与验证。具体而言，我们提出了三种在给定测量数据下利用代理模型进行贝叶斯推断的方法。这是一项代理模型不确定性传播尤为相关的任务，因为若未能考虑该不确定性，可能导致对目标参数的估计存在偏差和/或过度自信。我们通过三个针对线性和非线性实际建模场景的详细案例研究展示了所提方法。代理模型中的不确定性传播能够实现对昂贵仿真器更可靠、更安全的近似，因此将在多个应用领域发挥作用。