Surrogate models are often used as computationally efficient approximations to complex simulation models, enabling tasks such as solving inverse problems, sensitivity analysis, and probabilistic forward predictions, which would otherwise be computationally infeasible. During training, surrogate parameters are fitted such that the surrogate reproduces the simulation model's outputs as closely as possible. However, the simulation model itself is merely a simplification of the real-world system, often missing relevant processes or suffering from misspecifications e.g., in inputs or boundary conditions. Hints about these might be captured in real-world measurement data, and yet, we typically ignore those hints during surrogate building. In this paper, we propose two novel probabilistic approaches to integrate simulation data and real-world measurement data during surrogate training. The first method trains separate surrogate models for each data source and combines their predictive distributions, while the second incorporates both data sources by training a single surrogate. We show the conceptual differences and benefits of the two approaches through both synthetic and real-world case studies. The results demonstrate the potential of these methods to improve predictive accuracy, predictive coverage, and to diagnose problems in the underlying simulation model. These insights can improve system understanding and future model development.

翻译：代理模型常被用作复杂仿真模型的计算高效近似，从而支持诸如求解反问题、敏感性分析和概率性前向预测等原本计算不可行的任务。在训练过程中，代理模型的参数被拟合，以使其尽可能精确地复现仿真模型的输出。然而，仿真模型本身仅是真实世界系统的简化表示，常常遗漏相关物理过程或存在输入参数、边界条件等方面的误设。关于这些缺陷的线索可能蕴含在真实世界的观测数据中，但我们在构建代理模型时通常忽略这些信息。本文提出了两种新颖的概率方法，在代理模型训练过程中融合仿真数据与真实世界观测数据。第一种方法为每个数据源分别训练独立的代理模型，并通过融合其预测分布实现集成；第二种方法则通过训练单一代理模型同时纳入两类数据源。我们通过合成案例与真实案例研究，阐明了两种方法在概念上的差异及其各自优势。结果表明，这些方法在提升预测精度、改善预测覆盖范围以及诊断底层仿真模型缺陷方面具有显著潜力。相关见解有助于深化对系统的理解并指导未来的模型开发。