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 two detailed case studies for both linear and nonlinear 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：替代模型是对更复杂仿真模型的统计或概念近似。在此背景下，将有限仿真预算及替代模型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，量化并传播替代模型的不确定性通常局限于特殊解析情形，否则计算成本极高。本文提出了一种可扩展的贝叶斯替代建模框架，实现了全面的不确定性量化、传播与验证。具体而言，我们提出了三种基于替代模型进行测量数据贝叶斯推断的方法。在此类任务中，替代模型不确定性的传播尤为重要，因为未能考虑该不确定性可能导致对目标参数的估计产生偏差和/或过度自信。我们通过线性与非线性建模场景的两个详细案例研究展示了该方法。替代模型中的不确定性传播能够实现对昂贵模拟器更可靠、更安全的近似，因而将在多个应用领域发挥重要作用。