Using Machine Learning to Make Long-term Predictions of Chaotic Time Series​*

Chaotic systems exhibit aperiodic behavior due to nonlinear components and are sensitive to initial conditions. This aperiodic behavior makes it difficult to predict the long-term behavior of chaotic systems. Sophisticated machine learning models are already studying the long-term prediction of chaotic systems. In this research, we investigate whether the simplest machine learning models can make long-term predictions that can compete with complex machine learning models such as reservoir computers.

We used the Lorenz equations as our model chaotic system. We took time series data of the Lorenz equations, trained machine learning models on the first part of the series, and used the remainder to test the model's prediction. We defined the length of predicted data that matches the test data as the valid time. We compared the valid times found using the following models: Linear Regression, Polynomial Regression, Support Vector Machine, and Random Forest. Random Forest gave the longest valid time prediction. However, the valid time produced by the Random Forest was not as long as those found using more complex machine learning models.