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首页> 外文期刊>SIAM/ASA Journal on Uncertainty Quantification >Representing Model Inadequacy: A Stochastic Operator Approach
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Representing Model Inadequacy: A Stochastic Operator Approach

机译：代表模型不足:一个随机操作方法

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摘要

Mathematical models of physical systems are subject to many uncertainties such as measurement errors and uncertain initial and boundary conditions. After accounting for these uncertainties, it is often revealed that discrepancies between the model output and the observations remain; if so, the model is said to be inadequate. In practice, the inadequate model may be the best that is available or tractable, and so it may be necessary to use the model for prediction despite its inadequacy. In this case, a representation of the inadequacy is necessary, so the impact of the observed discrepancy can be determined. We investigate this problem in the context of chemical kinetics and propose a new technique to account for model inadequacy that is both probabilistic and physically meaningful. A stochastic inadequacy operator S is introduced which is embedded in the ODEs describing the evolution of chemical species concentrations and which respects certain physical constraints such as conservation laws. The parameters of S are governed by probability distributions, which in turn are characterized by a set of hyperparameters. The model parameters and hyperparameters are calibrated using high-dimensional hierarchical Bayesian inference. We apply the method to a typical problem in chemical kinetics|the reaction mechanism of hydrogen combustion.
机译：物理系统的数学模型测量等许多不确定因素错误和不确定的初始和边界条件。不确定性,它通常是显示模型输出之间的差异观察保持;还不够。可能是最好的可用的或容易处理的,所以可能需要使用模型预测尽管其不足。不足的表示是必要的,所以可以观察到的差异的影响确定。化学动力学和提出一个新的技术占模型不足概率和物理意义。介绍了随机不足运营商年代嵌入在常微分方程描述的是哪个进化化学物种浓度和哪方面等物理约束守恒定律。由概率分布,特点是一组hyperparameters。hyperparameters校准使用高维层次贝叶斯推理。我们应用的一个典型问题的方法化学动力学|的反应机理氢燃烧。

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