DeepAI AI Chat
Log In Sign Up

Predicting discrete-time bifurcations with deep learning

by   Thomas M. Bury, et al.

Many natural and man-made systems are prone to critical transitions – abrupt and potentially devastating changes in dynamics. Deep learning classifiers can provide an early warning signal (EWS) for critical transitions by learning generic features of bifurcations (dynamical instabilities) from large simulated training data sets. So far, classifiers have only been trained to predict continuous-time bifurcations, ignoring rich dynamics unique to discrete-time bifurcations. Here, we train a deep learning classifier to provide an EWS for the five local discrete-time bifurcations of codimension-1. We test the classifier on simulation data from discrete-time models used in physiology, economics and ecology, as well as experimental data of spontaneously beating chick-heart aggregates that undergo a period-doubling bifurcation. The classifier outperforms commonly used EWS under a wide range of noise intensities and rates of approach to the bifurcation. It also predicts the correct bifurcation in most cases, with particularly high accuracy for the period-doubling, Neimark-Sacker and fold bifurcations. Deep learning as a tool for bifurcation prediction is still in its nascence and has the potential to transform the way we monitor systems for critical transitions.


page 15

page 18

page 19


Continuous and Discrete-Time Survival Prediction with Neural Networks

Application of discrete-time survival methods for continuous-time surviv...

Periodic attractor in the discrete time best-response dynamics of the Rock-Paper-Scissors game

The Rock-Paper-Scissors (RPS) game is a classic non-cooperative game wid...

On the relationships between Z-, C-, and H-local unitaries

Quantum walk algorithms can speed up search of physical regions of space...

Universal Early Warning Signals of Phase Transitions in Climate Systems

The potential for complex systems to exhibit tipping points in which an ...

Discrete time stochastic and deterministic Petri box calculus

We propose an extension with deterministically timed multiactions of dis...

Deep Learning of Conjugate Mappings

Despite many of the most common chaotic dynamical systems being continuo...