Prediction of chaotic attractors in quasiperiodically forced logistic map using deep learning
This work addresses chaotic system prediction for researchers in nonlinear dynamics, but it is incremental as it applies an existing method (LSTM) to a specific dataset.
The authors tackled the problem of forecasting chaotic attractors in a quasiperiodically forced logistic map using Long Short-Term Memory (LSTM) deep learning, achieving good performance in predicting chaotic dynamics up to three steps as evaluated by Root Mean Square Error.
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.