Prediction of chaotic attractors in quasiperiodically forced logistic map using deep learning

TL;DR

This paper demonstrates that Long Short-Term Memory deep learning models can effectively forecast chaotic attractors in a quasiperiodically forced logistic map, achieving accurate multi-step predictions.

Contribution

It introduces a deep learning approach using LSTM to predict chaotic dynamics in a specific nonlinear system, with analysis of model robustness and multi-step forecasting capabilities.

Findings

LSTM models accurately predict up to three steps ahead.

Model robustness depends on the number of units in LSTM layers.

Deep learning effectively captures chaotic attractor dynamics.

Abstract

We forecast two different chaotic dynamics of the quasiperiodically forced logistic map using the well-known deep learning framework Long Short-Term Memory. We generate two data sets and use one in the training process and the other in the testing process. The predicted values are evaluated using the metric called Root Mean Square Error and visualized using the scatter plots. The robustness of the Long Short-Term Memory model is evaluated using the number of units in the layers of the model. We also make multi-step forecasting of the considered system. We show that the considered Long Short-Term Memory model performs well in predicting chaotic attractors upto three steps.