mlsanityData to 14 Oct 2026

Predicting discrete-time bifurcations with deep learning

arXiv 2303.09669 ↗First posted 16 Mar 2023q-bio.QM cs.LG math.DScited by 13

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Abstract (arXiv)

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.

Key facts. Cited by 13 papers in the map (data through 14 Oct 2026). Builds on 6 of its 61 references that are in the map. First posted on arXiv 16 Mar 2023.

Builds on

6 of 61 references.

References · 6

  1. 2017Attention Is All You Needcited by 60,361
  2. 2013Visualizing and Understanding Convolutional Networkscited by 2,290
  3. 2022Transformers in Time Series: A Surveycited by 497
  4. 2020Machine learning prediction of critical transition and system collapsecited by 54
  5. 2022Using Machine Learning to Anticipate Tipping Points and Extrapolate to Post-Tipping Dynamics of Non-Stationary Dynamical Systemscited by 33
  6. 2022Universal Early Warning Signals of Phase Transitions in Climate Systemscited by 10

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 6; 2025: 3; 2026: 2.

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  1. 2024Out-of-Domain Generalization in Dynamical Systems Reconstructioncited by 33
  2. 2024Deep Learning for predicting rate-induced tippingcited by 8
  3. 2025Neural Ordinary Differential Equations for Learning and Extrapolating System Dynamics Across Bifurcationscited by 4
  4. 2023Let's do the time-warp-attend: Learning topological invariants of dynamical systemscited by 2
  5. 2024Deep learning for predicting the occurrence of tipping pointscited by 2
  6. 2024Comparative Analysis of Predicting Subsequent Steps in H'enon Mapcited by 1
  7. 2023Fold Bifurcation Identification through Scientific Machine Learningcited by 0
  8. 2024Deep Learning for Prediction and Classifying the Dynamical behaviour of Piecewise Smooth Mapscited by 0
  9. 2024Learning from the past: predicting critical transitions with machine learning trained on surrogates of historical datacited by 0
  10. 2025Echoes Before Collapse: Deep Learning Detection of Flickering in Complex Systemscited by 0
  11. 2025MODE: Learning compositional representations of complex systems with Mixtures Of Dynamical Expertscited by 0
  12. 2026Machine Learning for Complex Systems Dynamics: Detecting Bifurcations in Dynamical Systems with Deep Neural Networkscited by 0
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  1. 2026GeomHerd: A Forward-looking Herding Quantification via Ricci Flow Geometry on Agent Interactive Simulationscited by 0