Kernel Analog Forecasting: Multiscale Test Problems
This work addresses the interpretation of predictions for researchers and practitioners using data-driven methods in multiscale systems, but it is incremental as it applies existing methods to new test problems.
The paper tackled the problem of interpreting data-driven predictions in multiscale dynamical systems by analyzing kernel analog forecasting methods, showing how predictions depend on whether variables are Markovian or non-Markovian and providing practical guidance.
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.