mlsanityData to 7 Oct 2026

Next Generation Reservoir Computing

arXiv 2106.07688 ↗First posted 14 Jun 2021cs.LG nlin.AOcited by 160

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Abstract (arXiv)

Reservoir computing is a best-in-class machine learning algorithm for processing information generated by dynamical systems using observed time-series data. Importantly, it requires very small training data sets, uses linear optimization, and thus requires minimal computing resources. However, the algorithm uses randomly sampled matrices to define the underlying recurrent neural network and has a multitude of metaparameters that must be optimized. Recent results demonstrate the equivalence of reservoir computing to nonlinear vector autoregression, which requires no random matrices, fewer metaparameters, and provides interpretable results. Here, we demonstrate that nonlinear vector autoregression excels at reservoir computing benchmark tasks and requires even shorter training data sets and training time, heralding the next generation of reservoir computing.

Key facts. Cited by 160 papers in the map (data through 7 Oct 2026). Builds on 13 of its 39 references that are in the map. First posted on arXiv 14 Jun 2021.

Builds on

13 of 39 references.

References · 13

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  2. 2019Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamicscited by 132
  3. 2018Reservoir Computing Universality With Stochastic Inputscited by 48
  4. 2019Forecasting Chaotic Systems with Very Low Connectivity Reservoir Computerscited by 43
  5. 2020Combining Machine Learning with Knowledge-Based Modeling for Scalable Forecasting and Subgrid-Scale Closure of Large, Complex, Spatiotemporal Systemscited by 23
  6. 2020Echo State Networks trained by Tikhonov least squares are L2(μ) approximators of ergodic dynamical systemscited by 21
  7. 2021Using Data Assimilation to Train a Hybrid Forecast System that Combines Machine-Learning and Knowledge-Based Componentscited by 18
  8. 2019How Entropic Regression Beats the Outliers Problem in Nonlinear System Identificationcited by 14
  9. 2016Bayesian optimization of hyper-parameters in reservoir computingcited by 13
  10. 2016Determination of the edge of criticality in echo state networks through Fisher information maximizationcited by 12
  11. 2020Model-Free Control of Dynamical Systems with Deep Reservoir Computingcited by 12
  12. 2020Bayesian optimisation of large-scale photonic reservoir computerscited by 7
1 more
  1. 2020Accuracy of neural networks for the simulation of chaotic dynamics: precision of training data vs precision of the algorithmcited by 7

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 8; 2022: 18; 2023: 30; 2024: 33; 2025: 46; 2026: 25.

160 papers.

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  1. 2023Machine learning with data assimilation and uncertainty quantification for dynamical systems: a reviewcited by 74
  2. 2021A Framework for Machine Learning of Model Error in Dynamical Systemscited by 37
  3. 2024Out-of-Domain Generalization in Dynamical Systems Reconstructioncited by 33
  4. 2023Training an Ising Machine with Equilibrium Propagationcited by 29
  5. 2023Model scale versus domain knowledge in statistical forecasting of chaotic systemscited by 27
  6. 2024Zero-shot forecasting of chaotic systemscited by 25
  7. 2023A Survey on Reservoir Computing and its Interdisciplinary Applications Beyond Traditional Machine Learningcited by 22
  8. 2021Model-free inference of unseen attractors: Reconstructing phase space features from a single noisy trajectory using reservoir computingcited by 21
  9. 2021Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observationscited by 20
  10. 2022Learning Spatiotemporal Chaos Using Next-Generation Reservoir Computingcited by 20
  11. 2022Parsimonious Physics-Informed Random Projection Neural Networks for Initial-Value Problems of ODEs and index-1 DAEscited by 19
  12. 2021Learning strange attractors with reservoir systemscited by 16
38 more
  1. 2023Analogue and Physical Reservoir Computing Using Water Wavescited by 16
  2. 2025Context parroting: A simple but tough-to-beat baseline for foundation models in scientific machine learningcited by 14
  3. 2022Integrating Multimodal Data for Joint Generative Modeling of Complex Dynamicscited by 13
  4. 2023Model-free tracking control of complex dynamical trajectories with machine learningcited by 13
  5. 2022Learning unseen coexisting attractorscited by 12
  6. 2025Panda: A pretrained forecast model for chaotic dynamicscited by 12
  7. 2022Catch-22s of reservoir computingcited by 11
  8. 2024Controlling Chaos Using Edge Computing Hardwarecited by 11
  9. 2023Embedding Theory of Reservoir Computing and Reducing Reservoir Network Using Time Delayscited by 10
  10. 2023Extrapolating tipping points and simulating non-stationary dynamics of complex systems using efficient machine learningcited by 9
  11. 2024Classical and Quantum Physical Reservoir Computing for Onboard Artificial Intelligence Systems: A Perspectivecited by 9
  12. 2024Data-driven model discovery with Kolmogorov-Arnold networkscited by 9
  13. 2024Infinite-dimensional next-generation reservoir computingcited by 9
  14. 2022Reservoir kernels and Volterra seriescited by 8
  15. 2024Koopman-informed recurrent neural networkscited by 8
  16. 2022Exploring the limits of multifunctionality across different reservoir computerscited by 7
  17. 2023Controlling Chaotic Maps using Next-Generation Reservoir Computingcited by 7
  18. 2023Quantum-Inspired Neural Network Model of Optical Illusionscited by 7
  19. 2024Chaotic attractor reconstruction using small reservoirs -- the influence of topologycited by 7
  20. 2024Recurrent Stochastic Configuration Networks for Temporal Data Analyticscited by 7
  21. 2024Hyperparameter Optimization for Randomized Algorithms: A Case Study on Random Featurescited by 7
  22. 2025Learning dynamical systems with hit-and-run random feature mapscited by 7
  23. 2021Neural Echo State Network using oscillations of gas bubbles in watercited by 6
  24. 2023Forecasting trends in food security with real time datacited by 6
  25. 2024Hybridizing Traditional and Next-Generation Reservoir Computing to Accurately and Efficiently Forecast Dynamical Systemscited by 6
  26. 2023Quantum Next Generation Reservoir Computing: An Efficient Quantum Algorithm for Forecasting Quantum Dynamicscited by 5
  27. 2023Learning noise-induced transitions by multi-scaling reservoir computingcited by 5
  28. 2024Physical Reservoir Computing Enabled by Solitary Waves and Biologically-Inspired Nonlinear Transformation of Input Datacited by 5
  29. 2024How more data can hurt: Instability and regularization in next-generation reservoir computingcited by 5
  30. 2022Recurrent Spectral Network (RSN): shaping the basin of attraction of a discrete map to reach automated classificationcited by 4
  31. 2023Inferring Attracting Basins of Power System with Machine Learningcited by 4
  32. 2023Machine-learning parameter tracking with partial state observationcited by 4
  33. 2024Machine Learning for Predicting Chaotic Systemscited by 4
  34. 2025Unsupervised learning for anticipating critical transitionscited by 4
  35. 2021Master memory function for delay-based reservoir computers with single-variable dynamicscited by 3
  36. 2021Learn one size to infer all: Exploiting translational symmetries in delay-dynamical and spatio-temporal systems using scalable neural networkscited by 3
  37. 2022On the effectiveness of Randomized Signatures as Reservoir for Learning Rough Dynamicscited by 3
  38. 2022`Next Generation' Reservoir Computing: an Empirical Data-Driven Expression of Dynamical Equations in Time-Stepping Formcited by 3

50 most cited of 160 All 160 (JSON)