多尺度模式的半侵入式不确定性传播
Semi-intrusive uncertainty propagation for multiscale models
摘要：
介绍了一类多尺度模式的半介入不确定性传播方法。该方法是半侵入性的，在这个意义上，该模型的检查被限制到单尺度系统的水平，并将这些单尺度组件视为黑盒。我们的目标是在减少的时间量相比，黑箱蒙特卡罗（MC）的多尺度模型的结果估计的不确定性。在所得到的半侵入式MC方法中，为了减少整个UP的执行时间，将昂贵的单尺度模型所需的样本数量最小化。在元建模方法中，昂贵的模型组件完全被计算上便宜得多的代理模型所取代。这些半侵入式算法已经过测试的反应扩散动力学的基础上的两个案例研究。结果表明，所提出的半侵入式方法可以导致在一个显着减少的计算时间多尺度UP，同时仍然准确地计算不确定性的估计。因此，半侵入式方法可以是一个有效的替代方案，当一个多尺度模型的不确定性不能估计的黑箱MC方法在一个可行的时间量。
英文摘要：
A family of semi-intrusive uncertainty propagation (UP) methods for multiscale models is introduced. The methods are semi-intrusive in the sense that inspection of the model is limited up to the level of the single scale systems, and viewing these single scale components as black-boxes. The goal is to estimate uncertainty in the result of multiscale models at a reduced amount of time as compared to black-box Monte Carlo (MC). In the resulting semi-intrusive MC method, the required number of samples of an expensive single scale model is minimized in order to reduce the execution time for the overall UP. In the metamodeling approach, the expensive model component is replaced completely by a computationally much cheaper surrogate model. These semi-intrusive algorithms have been tested on two case studies based on reaction-diffusion dynamics. The results demonstrate that the proposed semi-intrusive methods can result in a significant reduction of the computational time for multiscale UP, while still computing accurately the estimates of uncertainties. The semi-intrusive methods can, therefore, be a valid alternative, when uncertainties of a multiscale model cannot be estimated by the black-box MC methods in a feasible amount of time.
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