Many computer models possess high-dimensional input spaces and substantial computational time to produce a single model evaluation. Although such models are often ‘deterministic’, these models suffer from a wide range of uncertainties. We argue that uncertainty quantification is crucial for computer model validation and reproducibility. We present a statistical framework, termed history matching, for performing global parameter search by comparing model output to the observed data. We employ Gaussian process (GP) emulators to produce fast predictions about model behaviour at the arbitrary input parameter settings allowing output uncertainty distributions to be calculated. History matching identifies sets of input parameters that give rise to acceptable matches between observed data and model output given our representation of uncertainties. Modellers could proceed by simulating computer models’ outputs of interest at these identified parameter settings and producing a range of predictions. The variability in model results is crucial for inter-model comparison as well as model development. We illustrate the performance of emulation and history matching on a simple one-dimensional toy model and in application to a climate model.

This article is part of the theme issue ‘Reliability and reproducibility in computational science: implementing verification, validation and uncertainty quantification in silico’.

许多计算机模型拥有高维输入空间和大量计算时间来产生单个模型评估。尽管此类模型通常是“确定性的”，但这些模型存在广泛的不确定性。我们认为不确定性量化对于计算机模型的验证和再现性至关重要。我们提出了一个称为历史匹配的统计框架，用于通过将模型输出与观察到的数据进行比较来执行全局参数搜索。我们采用高斯过程 (GP) 仿真器在任意输入参数设置下生成关于模型行为的快速预测，从而允许计算输出不确定性分布。鉴于我们对不确定性的表示，历史匹配确定了在观测数据和模型输出之间产生可接受匹配的输入参数集。建模者可以通过在这些确定的参数设置下模拟计算机模型的感兴趣输出并产生一系列预测来继续进行。模型结果的可变性对于模型间比较和模型开发至关重要。我们说明了模拟和历史匹配在一个简单的一维玩具模型上的性能以及在气候模型中的应用。

本文是主题问题“计算科学中的可靠性和再现性：在计算机中实现验证、确认和不确定性量化”的一部分。