Predicting discrete-time bifurcations with deep learning

Area of Science:

• Complex Systems Science
• Machine Learning
• Dynamical Systems Theory

Background:

• Natural and man-made systems can undergo abrupt critical transitions.
• Early warning signals for these transitions are crucial for prediction and mitigation.
• Current deep learning models primarily focus on continuous-time bifurcations, neglecting discrete-time dynamics.

Purpose of the Study:

• To train a deep learning classifier for early warning signals of discrete-time bifurcations.
• To evaluate the classifier's performance on diverse simulation and experimental data.
• To compare the deep learning approach against established early warning signals.

Main Methods:

• Developed a deep learning classifier trained on simulated data for five local discrete-time bifurcations.
• Tested the classifier using discrete-time models from physiology, economics, and ecology.
• Validated performance on experimental data from chick-heart aggregates exhibiting period-doubling bifurcations.

Main Results:

• The deep learning classifier demonstrated superior sensitivity and specificity over common early warning signals.
• Performance was robust across various noise intensities and rates of approach to bifurcation.
• Accurate prediction of specific bifurcations, including period-doubling, Neimark-Sacker, and fold bifurcations, was achieved.

Conclusions:

• Deep learning effectively predicts discrete-time bifurcations, offering a powerful tool for early warning.
• This approach surpasses traditional methods in accuracy and robustness.
• Deep learning holds significant potential to revolutionize the monitoring of systems for critical transitions.