SIAM/ASA Journal on Uncertainty Quantification, Volume 8, Issue 3, Page 1118-1138, January 2020.
All observable phenomena can be described by alternative mathematical models, which vary in their fidelity and computational cost. Selection of an appropriate model involves a tradeoff between computational cost and representational accuracy. Ubiquitous uncertainty (randomness) in model parameters and forcings, and assimilation of observations of the system states into predictions, complicate the model selection problem. We present a framework for analysis of the impact of data assimilation on cost-constrained model selection. The framework relies on the definitions of cost and accuracy functions in the context of data assimilation for multifidelity models with uncertain (random) coefficients. It contains an estimate of error bounds for a system's state prediction obtained by assimilating data into a model via an ensemble Kalman filter. This estimate is given in terms of model error, sampling error, and data error. Two examples illustrating the applicability of our model selection method are provided. The first example deals with an ordinary differential equation, for which a sequence of lower-fidelity models is constructed by progressively increasing the time step used in its discretization. The second example comprises the viscous Burgers equation as the high-fidelity model and a linear advection-diffusion equation as its low-fidelity counterpart.

中文翻译：

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不确定性传播和数据同化的资源受限模型选择

SIAM / ASA不确定性量化期刊，第8卷，第3期，第1118-1138页，2020年1月。
所有可观察到的现象都可以通过替代的数学模型来描述，这些模型的保真度和计算成本各不相同。选择合适的模型需要在计算成本和表示精度之间进行权衡。模型参数和强迫的普遍不确定性（随机性）以及将系统状态的观测值同化为预测值会使模型选择问题复杂化。我们提出了一个框架，用于分析数据同化对成本受限的模型选择的影响。对于具有不确定（随机）系数的多保真度模型，在数据同化的背景下，框架依赖于成本和准确性函数的定义。它包含系统状态预测的误差范围的估计值，该误差范围是通过集成卡尔曼滤波器将数据同化到模型中而获得的。该估计是根据模型误差，采样误差和数据误差给出的。提供了两个示例，说明我们的模型选择方法的适用性。第一个示例涉及一个常微分方程，通过逐步增加离散化所用的时间步长，可以构造一系列低保真模型。第二个示例包括作为高保真度模型的粘性Burgers方程和作为其低保真度模型的线性对流扩散方程。通过逐步增加离散化过程中使用的时间步长，可以构建一系列低保真模型。第二个示例包括作为高保真度模型的粘性Burgers方程和作为其低保真度模型的线性对流扩散方程。通过逐步增加离散化过程中使用的时间步长，可以构建一系列低保真模型。第二个示例包括作为高保真度模型的粘性Burgers方程和作为其低保真度模型的线性对流扩散方程。