mlsanityData to 7 Oct 2026

Forecasting Chaotic Systems with Very Low Connectivity Reservoir Computers

arXiv 1910.00659 ↗First posted 1 Oct 2019cs.LG nlin.CD stat.MLcited by 43

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Abstract (arXiv)

We explore the hyperparameter space of reservoir computers used for forecasting of the chaotic Lorenz '63 attractor with Bayesian optimization. We use a new measure of reservoir performance, designed to emphasize learning the global climate of the forecasted system rather than short-term prediction. We find that optimizing over this measure more quickly excludes reservoirs that fail to reproduce the climate. The results of optimization are surprising: the optimized parameters often specify a reservoir network with very low connectivity. Inspired by this observation, we explore reservoir designs with even simpler structure, and find well-performing reservoirs that have zero spectral radius and no recurrence. These simple reservoirs provide counterexamples to widely used heuristics in the field, and may be useful for hardware implementations of reservoir computers.

Key facts. Cited by 43 papers in the map (data through 7 Oct 2026). First posted on arXiv 1 Oct 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 10; 2022: 6; 2023: 9; 2024: 8; 2025: 4; 2026: 6.

43 papers.

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  1. 2021Next Generation Reservoir Computingcited by 160
  2. 2022Using Machine Learning to Anticipate Tipping Points and Extrapolate to Post-Tipping Dynamics of Non-Stationary Dynamical Systemscited by 33
  3. 2021Robust Optimization and Validation of Echo State Networks for learning chaotic dynamicscited by 27
  4. 2021Anticipating synchronization with machine learningcited by 22
  5. 2021Adaptable Hamiltonian neural networkscited by 21
  6. 2021Integrating Recurrent Neural Networks with Data Assimilation for Scalable Data-Driven State Estimationcited by 20
  7. 2022Catch-22s of reservoir computingcited by 11
  8. 2023Embedding Theory of Reservoir Computing and Reducing Reservoir Network Using Time Delayscited by 10
  9. 2024Data-driven model discovery with Kolmogorov-Arnold networkscited by 9
  10. 2021Symmetry-Aware Reservoir Computingcited by 7
  11. 2024Chaotic attractor reconstruction using small reservoirs -- the influence of topologycited by 7
  12. 2024Hyperparameter Optimization for Randomized Algorithms: A Case Study on Random Featurescited by 7
31 more
  1. 2023Constraining Chaos: Enforcing dynamical invariants in the training of recurrent neural networkscited by 6
  2. 2023Forecasting trends in food security with real time datacited by 6
  3. 2024Hybridizing Traditional and Next-Generation Reservoir Computing to Accurately and Efficiently Forecast Dynamical Systemscited by 6
  4. 2021Controlling nonlinear dynamical systems into arbitrary states using machine learningcited by 5
  5. 2021Cluster-based Input Weight Initialization for Echo State Networkscited by 4
  6. 2023Machine-learning parameter tracking with partial state observationcited by 4
  7. 2022`Next Generation' Reservoir Computing: an Empirical Data-Driven Expression of Dynamical Equations in Time-Stepping Formcited by 3
  8. 2023Temporal Subsampling Diminishes Small Spatial Scales in Recurrent Neural Network Emulators of Geophysical Turbulencecited by 3
  9. 2021Learning Hamiltonian dynamics by reservoir computercited by 2
  10. 2022Digital twins of nonlinear dynamical systemscited by 2
  11. 2022Emergence of a stochastic resonance in machine learningcited by 2
  12. 2023Effect of temporal resolution on the reproduction of chaotic dynamics via reservoir computingcited by 2
  13. 2023Learning unidirectional coupling using echo-state networkcited by 2
  14. 2023Reservoir Computing with Error Correction: Long-term Behaviors of Stochastic Dynamical Systemscited by 2
  15. 2024Learning to learn ecosystems from limited data -- a meta-learning approachcited by 2
  16. 2024Reconstructing dynamics from sparse observations with no training on target systemcited by 2
  17. 2025Minimal Deterministic Echo State Networks Outperform Random Reservoirs in Learning Chaotic Dynamicscited by 2
  18. 2022Dimensional criterion for forecasting nonlinear systems by reservoir computingcited by 1
  19. 2023Digital twins of nonlinear dynamical systems: A perspectivecited by 1
  20. 2024Predicting Chaotic System Behavior using Machine Learning Techniquescited by 1
  21. 2025Machine-Precision Prediction of Low-Dimensional Chaotic Systems from Noise-Free Datacited by 1
  22. 2026On Dominant Manifolds in Reservoir Computing Networkscited by 1
  23. 2021Deep Chaos Synchronizationcited by 0
  24. 2024Stochastic parameter reduced-order model based on hybrid machine learning approachescited by 0
  25. 2025Federated Koopman-Reservoir Learning for Large-Scale Multivariate Time-Series Anomaly Detectioncited by 0
  26. 2025A tensor network approach for chaotic time series predictioncited by 0
  27. 2026Storage and selection of multiple chaotic attractors in minimal reservoir computerscited by 0
  28. 2026Vestibular reservoir computingcited by 0
  29. 2026Evolutionary Optimization Reveals Structural Constraints on Reservoir Architecture for Spatiotemporal Chaoscited by 0
  30. 2026Beyond the Edge of Chaos: Stability-Expressivity Transfer in Reservoir Forecastingcited by 0
  31. 2026Inference of Unknown Dynamical Components Using Next Generation Reservoir Computing: From Chaotic Systems to Climate Datacited by 0