Deep Learning for Nonlinear Time Series: Examples for Inferring Slow Driving Forces

Abstract

Records for observing dynamics are usually complied by a form of time series. However, time series can be a challenging type of dataset for deep neural networks to learn. In deep neural networks, pairs of inputs and outputs are usually fed for constructive mapping. Such inputs are typically prepared as static images in successful applications. And so, here we propose two methods to prepare such inputs for learning the dynamical properties behind time series. In the first method, we simply array a time series in the shape of a rectangle as an image. In the second method, we convert a time series into a distance matrix using delay coordinates, or an unthresholded recurrence plot. We demonstrate that the second method performs well in inferring a slow driving force from observations of a forced system within which there are symmetry and almost invariant subsets.