mlsanityData to 14 Oct 2026

Machine learning prediction of critical transition and system collapse

arXiv 2012.01545 ↗First posted 2 Dec 2020cs.LG cs.AI math.DScited by 54

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Abstract (arXiv)

To predict a critical transition due to parameter drift without relying on model is an outstanding problem in nonlinear dynamics and applied fields. A closely related problem is to predict whether the system is already in or if the system will be in a transient state preceding its collapse. We develop a model free, machine learning based solution to both problems by exploiting reservoir computing to incorporate a parameter input channel. We demonstrate that, when the machine is trained in the normal functioning regime with a chaotic attractor (i.e., before the critical transition), the transition point can be predicted accurately. Remarkably, for a parameter drift through the critical point, the machine with the input parameter channel is able to predict not only that the system will be in a transient state, but also the average transient time before the final collapse.

Key facts. Cited by 54 papers in the map (data through 14 Oct 2026). First posted on arXiv 2 Dec 2020.

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Citing papers per year: 2021: 5; 2022: 7; 2023: 9; 2024: 11; 2025: 11; 2026: 11.

54 papers.

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  1. 2022Using Machine Learning to Anticipate Tipping Points and Extrapolate to Post-Tipping Dynamics of Non-Stationary Dynamical Systemscited by 33
  2. 2024Zero-shot forecasting of chaotic systemscited by 28
  3. 2021Anticipating synchronization with machine learningcited by 22
  4. 2021Adaptable Hamiltonian neural networkscited by 21
  5. 2023Predicting discrete-time bifurcations with deep learningcited by 13
  6. 2023Model-free tracking control of complex dynamical trajectories with machine learningcited by 13
  7. 2022Catch-22s of reservoir computingcited by 11
  8. 2023Extrapolating tipping points and simulating non-stationary dynamics of complex systems using efficient machine learningcited by 9
  9. 2024Data-driven model discovery with Kolmogorov-Arnold networkscited by 9
  10. 2023Tipping Point Forecasting in Non-Stationary Dynamics on Function Spacescited by 8
  11. 2024How more data can hurt: Instability and regularization in next-generation reservoir computingcited by 5
  12. 2022Discovering dynamical features of Hodgkin-Huxley-type model of physiological neuron using artificial neural networkcited by 4
38 more
  1. 2023Inferring Attracting Basins of Power System with Machine Learningcited by 4
  2. 2023Machine-learning parameter tracking with partial state observationcited by 4
  3. 2025Unsupervised learning for anticipating critical transitionscited by 4
  4. 2025Neural Ordinary Differential Equations for Learning and Extrapolating System Dynamics Across Bifurcationscited by 4
  5. 2026Position: A Dynamical Systems Perspective is Needed to Advance Time Series Modelingcited by 4
  6. 2021Model-free prediction of emergence of extreme events in a parametrically driven nonlinear dynamical system by Deep Learningcited by 3
  7. 2021Learn one size to infer all: Exploiting translational symmetries in delay-dynamical and spatio-temporal systems using scalable neural networkscited by 3
  8. 2023Controlling dynamical systems to complex target states using machine learning: next-generation vs. classical reservoir computingcited by 3
  9. 2021Learning Hamiltonian dynamics by reservoir computercited by 2
  10. 2022Predicting extreme events from data using deep machine learning: when and wherecited by 2
  11. 2022Digital twins of nonlinear dynamical systemscited by 2
  12. 2022Emergence of a stochastic resonance in machine learningcited by 2
  13. 2024Deep learning for predicting the occurrence of tipping pointscited by 2
  14. 2024Learning to learn ecosystems from limited data -- a meta-learning approachcited by 2
  15. 2025Tailored Forecasting from Short Time Series via Meta-learningcited by 2
  16. 2025Learning Beyond Experience: Generalizing to Unseen State Space with Reservoir Computingcited by 2
  17. 2025Multifunctional physical reservoir computing in soft tensegrity robotscited by 2
  18. 2026Ultra-Early Prediction of Tipping Points: Integrating Dynamical Measures with Reservoir Computingcited by 2
  19. 2023Digital twins of nonlinear dynamical systems: A perspectivecited by 1
  20. 2023Tipping Points of Evolving Epidemiological Networks: Machine Learning-Assisted, Data-Driven Effective Modelingcited by 1
  21. 2024Thermodynamic limit in learning period threecited by 1
  22. 2025Versatile Reservoir Computing for Heterogeneous Complex Networkscited by 1
  23. 2022Changes from Classical Statistics to Modern Statistics and Data Sciencecited by 0
  24. 2024Machine-learning prediction of tipping with applications to the Atlantic Meridional Overturning Circulationcited by 0
  25. 2024Adaptive control of recurrent neural networks using conceptorscited by 0
  26. 2024Prediction of Unobserved Bifurcation by Unsupervised Extraction of Slowly Time-Varying System Parameter Dynamics from Time Series Using Reservoir Computingcited by 0
  27. 2024Reconstruction of neuromorphic dynamics from a single scalar time series using variational autoencoder and neural network mapcited by 0
  28. 2024Controlling Dynamical Systems into Unseen Target States Using Machine Learningcited by 0
  29. 2025On the dimension of pullback attractors in recurrent neural networkscited by 0
  30. 2025Attractor-merging Crises and Intermittency in Reservoir Computingcited by 0
  31. 2025Attractor learning for spatiotemporally chaotic dynamical systems using echo state networks with transfer learningcited by 0
  32. 2025Deficiency of equation-finding approach to data-driven modeling of dynamical systemscited by 0
  33. 2025Noise-robust Contrastive Learning for Critical Transition Detection in Dynamical Systemscited by 0
  34. 2026Storage and selection of multiple chaotic attractors in minimal reservoir computerscited by 0
  35. 2026Anticipating tipping in spatiotemporal systems with machine learningcited by 0
  36. 2026Vestibular reservoir computingcited by 0
  37. 2026Inferring bifurcation diagrams of two distinct chaotic systems by a single machinecited by 0
  38. 2026Topological Out-of-Domain Generalization in Dynamical Systems Reconstructioncited by 0

50 most cited of 54 All 54 (JSON)