An Application of Convolutional Neural Networks to Chaotic Systems

We propose a novel method of analyzing dynamic systems for chaotic behavior using machine learning techniques. The study of chaos in dynamic systems often involves analyzing visual representations of data points generated by the systems. One method includes embedding one-dimensional time-series data into a two-dimensional space (a "pq diagram") as an interim step in the test for chaotic behavior. We study the application of a machine learning visual recognition model—a Convolutional Neural Network—on the pq diagrams generated in various systems and determine that they can be used to reliably differentiate chaotic and periodic systems from one another, and possibly to differentiate between different types of chaotic systems themselves.