KERNEL ANALOG FORECASTING: MULTISCALE TEST PROBLEMS
KERNEL ANALOG FORECASTING: MULTISCALE TEST PROBLEMS
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DOI：
10.1137/20m1338289
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发表时间：
2021-01-01
影响因子：
1.6
通讯作者：
Stuart, Andrew
中科院分区：
文献类型：
--
作者：
Burov, Dmitry;Giannakis, Dimitrios;Stuart, Andrew
随着可用数据量的增长以及算法发展与之相匹配，数据驱动的预测正变得越来越普遍。所做预测的性质以及对其进行解读的方式，在很大程度上取决于为预测所选变量具有马尔可夫性或近似马尔可夫性的程度。多尺度系统提供了一个可对这一问题进行分析的框架。在这项研究中，从多尺度动力系统生成的数据角度出发，对核模拟预测方法展开研究。所选取的问题展现出多种不同的马尔可夫闭合情况，同时运用了平均化和均匀化方法；此外，还考虑了不存在尺度分离且预测变量不具有马尔可夫性的情形。这些研究为数据驱动预测方法在实际应用中的解读提供了指导。
Data-driven prediction is becoming increasingly widespread as the volume of data available grows and as algorithmic development matches this growth. The nature of the predictions made and the manner in which they should be interpreted depend crucially on the extent to which the variables chosen for prediction are Markovian or approximately Markovian. Multiscale systems provide a framework in which this issue can be analyzed. In this work kernel analog forecasting methods are studied from the perspective of data generated by multiscale dynamical systems. The problems chosen exhibit a variety of different Markovian closures, using both averaging and homogenization; furthermore, settings where scale separation is not present and the predicted variables are non-Markovian are also considered. The studies provide guidance for the interpretation of data-driven prediction methods when used in practice.