核模拟预测：多尺度测试问题
Kernel Analog Forecasting: Multiscale Test Problems
摘要：
随着可用数据量的增长以及算法的发展与此增长相匹配，数据驱动的预测正变得越来越普遍。预测的性质和解释的方式，关键取决于选择用于预测的变量在多大程度上是马尔可夫的，或者近似于马尔可夫。多尺度系统提供了一个框架，在其中可以分析这个问题。本文从多尺度动力系统产生数据的角度研究了核模拟预测方法。所选择的问题表现出各种不同的马尔可夫封闭，使用平均和均匀化;此外，尺度分离不存在和预测变量是非马尔可夫的设置，也被认为是。这些研究为在实践中使用数据驱动的预测方法提供了指导。
英文摘要：
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, depends 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
