# Predicting discrete-time bifurcations with deep learning

arXiv: https://arxiv.org/abs/2303.09669 · HTML: https://mlsanity.com/paper/2303.09669/

## 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 (most cited first, 6 of 6)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [Machine learning prediction of critical transition and system collapse](https://mlsanity.com/paper/2012.01545/) (2020)
- [Using Machine Learning to Anticipate Tipping Points and Extrapolate to Post-Tipping Dynamics of Non-Stationary Dynamical Systems](https://mlsanity.com/paper/2207.00521/) (2022)
- [Universal Early Warning Signals of Phase Transitions in Climate Systems](https://mlsanity.com/paper/2206.00060/) (2022)

## Built on by (most cited first, 13 of 13)

- [Out-of-Domain Generalization in Dynamical Systems Reconstruction](https://mlsanity.com/paper/2402.18377/) (2024)
- [Deep Learning for predicting rate-induced tipping](https://mlsanity.com/paper/2409.07590/) (2024)
- [Neural Ordinary Differential Equations for Learning and Extrapolating System Dynamics Across Bifurcations](https://mlsanity.com/paper/2507.19036/) (2025)
- [Let's do the time-warp-attend: Learning topological invariants of dynamical systems](https://mlsanity.com/paper/2312.09234/) (2023)
- [Deep learning for predicting the occurrence of tipping points](https://mlsanity.com/paper/2407.18693/) (2024)
- [Comparative Analysis of Predicting Subsequent Steps in H'enon Map](https://mlsanity.com/paper/2405.10190/) (2024)
- [Fold Bifurcation Identification through Scientific Machine Learning](https://mlsanity.com/paper/2312.14210/) (2023)
- [Deep Learning for Prediction and Classifying the Dynamical behaviour of Piecewise Smooth Maps](https://mlsanity.com/paper/2406.17001/) (2024)
- [Learning from the past: predicting critical transitions with machine learning trained on surrogates of historical data](https://mlsanity.com/paper/2410.09707/) (2024)
- [Echoes Before Collapse: Deep Learning Detection of Flickering in Complex Systems](https://mlsanity.com/paper/2509.04683/) (2025)
- [MODE: Learning compositional representations of complex systems with Mixtures Of Dynamical Experts](https://mlsanity.com/paper/2510.09594/) (2025)
- [Machine Learning for Complex Systems Dynamics: Detecting Bifurcations in Dynamical Systems with Deep Neural Networks](https://mlsanity.com/paper/2603.04420/) (2026)
- [GeomHerd: A Forward-looking Herding Quantification via Ricci Flow Geometry on Agent Interactive Simulations](https://mlsanity.com/paper/2605.11645/) (2026)

## 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.