论文标题
内核模拟预测：多尺度测试问题
Kernel Analog Forecasting: Multiscale Test Problems
论文作者
论文摘要
随着可用数据的增长和算法的开发与该增长相匹配，数据驱动的预测越来越普遍。提出的预测的性质及其应解释的方式取决于为预测选择的变量是马尔可夫人或大约是马尔可夫人。多尺度系统提供了一个可以分析此问题的框架。在这项工作中，从多尺度动力学系统生成的数据的角度研究了内核模拟预测方法。所选择的问题使用平均和均匀化表现出各种不同的马尔可夫封闭。此外，还考虑了不存在比例分离且预测变量是非马克维亚的设置。在实践中使用时，研究为解释数据驱动的预测方法提供了指导。
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, 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.
