# Anticipating synchronization with machine learning

arXiv: https://arxiv.org/abs/2103.13358 · HTML: https://mlsanity.com/paper/2103.13358/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 67 references that are in the map.
- First posted on arXiv 13 Mar 2021.

## Builds on (most cited first, 8 of 8)

- [A Critical Review of Recurrent Neural Networks for Sequence Learning](https://mlsanity.com/paper/1506.00019/) (2015)
- [Hybrid Forecasting of Chaotic Processes: Using Machine Learning in Conjunction with a Knowledge-Based Model](https://mlsanity.com/paper/1803.04779/) (2018)
- [Machine learning prediction of critical transition and system collapse](https://mlsanity.com/paper/2012.01545/) (2020)
- [Forecasting Chaotic Systems with Very Low Connectivity Reservoir Computers](https://mlsanity.com/paper/1910.00659/) (2019)
- [Model-free prediction of spatiotemporal dynamical systems with recurrent neural networks: Role of network spectral radius](https://mlsanity.com/paper/1910.04426/) (2019)
- [Machine-learning inference of fluid variables from data using reservoir computing](https://mlsanity.com/paper/1805.09917/) (2018)
- [Inferring the dynamics of oscillatory systems using recurrent neural networks](https://mlsanity.com/paper/1904.03026/) (2019)
- [Transfer learning of chaotic systems](https://mlsanity.com/paper/2011.09970/) (2020)

## Built on by (most cited first, 22 of 22)

- [Model-free tracking control of complex dynamical trajectories with machine learning](https://mlsanity.com/paper/2309.11470/) (2023)
- [Catch-22s of reservoir computing](https://mlsanity.com/paper/2210.10211/) (2022)
- [Deep Learning for predicting rate-induced tipping](https://mlsanity.com/paper/2409.07590/) (2024)
- [Exploring the limits of multifunctionality across different reservoir computers](https://mlsanity.com/paper/2205.11375/) (2022)
- [How more data can hurt: Instability and regularization in next-generation reservoir computing](https://mlsanity.com/paper/2407.08641/) (2024)
- [Inferring Attracting Basins of Power System with Machine Learning](https://mlsanity.com/paper/2305.14374/) (2023)
- [Machine-learning parameter tracking with partial state observation](https://mlsanity.com/paper/2311.09142/) (2023)
- [Unsupervised learning for anticipating critical transitions](https://mlsanity.com/paper/2501.01579/) (2025)
- [Learning Hamiltonian dynamics by reservoir computer](https://mlsanity.com/paper/2104.14474/) (2021)
- [Digital twins of nonlinear dynamical systems](https://mlsanity.com/paper/2210.06144/) (2022)
- [Emergence of a stochastic resonance in machine learning](https://mlsanity.com/paper/2211.09955/) (2022)
- [Learning to learn ecosystems from limited data -- a meta-learning approach](https://mlsanity.com/paper/2410.07368/) (2024)
- [Reconstructing dynamics from sparse observations with no training on target system](https://mlsanity.com/paper/2410.21222/) (2024)
- [Multifunctional physical reservoir computing in soft tensegrity robots](https://mlsanity.com/paper/2507.21496/) (2025)
- [Estimation of Correlation Matrices from Limited time series Data using Machine Learning](https://mlsanity.com/paper/2209.01198/) (2022)
- [Digital twins of nonlinear dynamical systems: A perspective](https://mlsanity.com/paper/2309.11461/) (2023)
- [Thermodynamic limit in learning period three](https://mlsanity.com/paper/2405.08825/) (2024)
- [Versatile Reservoir Computing for Heterogeneous Complex Networks](https://mlsanity.com/paper/2505.15219/) (2025)
- [A latent linear model for nonlinear coupled oscillators on graphs](https://mlsanity.com/paper/2311.14910/) (2023)
- [Fold Bifurcation Identification through Scientific Machine Learning](https://mlsanity.com/paper/2312.14210/) (2023)
- [Machine-learning prediction of tipping with applications to the Atlantic Meridional Overturning Circulation](https://mlsanity.com/paper/2402.14877/) (2024)
- [Inferring bifurcation diagrams of two distinct chaotic systems by a single machine](https://mlsanity.com/paper/2604.26632/) (2026)

## Abstract (arXiv)

In applications of dynamical systems, situations can arise where it is desired to predict the onset of synchronization as it can lead to characteristic and significant changes in the system performance and behaviors, for better or worse. In experimental and real settings, the system equations are often unknown, raising the need to develop a prediction framework that is model free and fully data driven. We contemplate that this challenging problem can be addressed with machine learning. In particular, exploiting reservoir computing or echo state networks, we devise a "parameter-aware" scheme to train the neural machine using asynchronous time series, i.e., in the parameter regime prior to the onset of synchronization. A properly trained machine will possess the power to predict the synchronization transition in that, with a given amount of parameter drift, whether the system would remain asynchronous or exhibit synchronous dynamics can be accurately anticipated. We demonstrate the machine-learning based framework using representative chaotic models and small network systems that exhibit continuous (second-order) or abrupt (first-order) transitions. A remarkable feature is that, for a network system exhibiting an explosive (first-order) transition and a hysteresis loop in synchronization, the machine learning scheme is capable of accurately predicting these features, including the precise locations of the transition points associated with the forward and backward transition paths.