mlsanityData to 7 Oct 2026

Catch-22s of reservoir computing

arXiv 2210.10211 ↗First posted 18 Oct 2022cs.LG cs.NE nlin.AOcited by 11

Not on the map. Why?

Abstract (arXiv)

Reservoir Computing (RC) is a simple and efficient model-free framework for forecasting the behavior of nonlinear dynamical systems from data. Here, we show that there exist commonly-studied systems for which leading RC frameworks struggle to learn the dynamics unless key information about the underlying system is already known. We focus on the important problem of basin prediction -- determining which attractor a system will converge to from its initial conditions. First, we show that the predictions of standard RC models (echo state networks) depend critically on warm-up time, requiring a warm-up trajectory containing almost the entire transient in order to identify the correct attractor. Accordingly, we turn to Next-Generation Reservoir Computing (NGRC), an attractive variant of RC that requires negligible warm-up time. By incorporating the exact nonlinearities in the original equations, we show that NGRC can accurately reconstruct intricate and high-dimensional basins of attraction, even with sparse training data (e.g., a single transient trajectory). Yet, a tiny uncertainty in the exact nonlinearity can render prediction accuracy no better than chance. Our results highlight the challenges faced by data-driven methods in learning the dynamics of multistable systems and suggest potential avenues to make these approaches more robust.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Builds on 31 of its 78 references that are in the map. First posted on arXiv 18 Oct 2022.

Builds on

31 of 78 references.

References · 31

  1. 2018Neural Ordinary Differential Equationscited by 3,733
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  3. 2017Visualizing the Loss Landscape of Neural Netscited by 1,126
  4. 2021Modern Koopman Theory for Dynamical Systemscited by 269
  5. 2021Next Generation Reservoir Computingcited by 160
  6. 2019Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamicscited by 132
  7. 2021Fit without fear: remarkable mathematical phenomena of deep learning through the prism of interpolationcited by 130
  8. 2020The Random Feature Model for Input-Output Maps between Banach Spacescited by 90
  9. 2020A Bayesian machine scientist to aid in the solution of challenging scientific problemscited by 61
  10. 2018Hybrid Forecasting of Chaotic Processes: Using Machine Learning in Conjunction with a Knowledge-Based Modelcited by 57
  11. 2020Machine learning prediction of critical transition and system collapsecited by 54
  12. 2018Reservoir Computing Universality With Stochastic Inputscited by 48
19 more
  1. 2019Forecasting Chaotic Systems with Very Low Connectivity Reservoir Computerscited by 43
  2. 2021A Framework for Machine Learning of Model Error in Dynamical Systemscited by 37
  3. 2019Model-free prediction of spatiotemporal dynamical systems with recurrent neural networks: Role of network spectral radiuscited by 34
  4. 2022Using Machine Learning to Anticipate Tipping Points and Extrapolate to Post-Tipping Dynamics of Non-Stationary Dynamical Systemscited by 33
  5. 2020Combining Machine Learning with Knowledge-Based Modeling for Scalable Forecasting and Subgrid-Scale Closure of Large, Complex, Spatiotemporal Systemscited by 23
  6. 2021Anticipating synchronization with machine learningcited by 22
  7. 2020Echo State Networks trained by Tikhonov least squares are L2(μ) approximators of ergodic dynamical systemscited by 21
  8. 2020Multifunctionality in a Reservoir Computercited by 21
  9. 2021Model-free inference of unseen attractors: Reconstructing phase space features from a single noisy trajectory using reservoir computingcited by 21
  10. 2021Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observationscited by 20
  11. 2020Do Reservoir Computers Work Best at the Edge of Chaos?cited by 17
  12. 2021Parallel Machine Learning for Forecasting the Dynamics of Complex Networkscited by 17
  13. 2018Using a reservoir computer to learn chaotic attractors, with applications to chaos synchronisation and cryptographycited by 16
  14. 2021Learning strange attractors with reservoir systemscited by 16
  15. 2018Rapid Time Series Prediction with a Hardware-Based Reservoir Computercited by 14
  16. 2022Optimizing Memory in Reservoir Computerscited by 13
  17. 2022Learning unseen coexisting attractorscited by 12
  18. 2020Machine Learning Link Inference of Noisy Delay-coupled Networks with Opto-Electronic Experimental Testscited by 7
  19. 2021Symmetry-Aware Reservoir Computingcited by 7

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 4; 2025: 4; 2026: 2.

11 papers.

  1. 2023Model scale versus domain knowledge in statistical forecasting of chaotic systemscited by 27
  2. 2024Zero-shot forecasting of chaotic systemscited by 25
  3. 2024How more data can hurt: Instability and regularization in next-generation reservoir computingcited by 5
  4. 2025On the emergence of numerical instabilities in Next Generation Reservoir Computingcited by 3
  5. 2024Learning to learn ecosystems from limited data -- a meta-learning approachcited by 2
  6. 2025Tailored Forecasting from Short Time Series via Meta-learningcited by 2
  7. 2025Learning Beyond Experience: Generalizing to Unseen State Space with Reservoir Computingcited by 2
  8. 2024Modeling Nonlinear Oscillator Networks Using Physics-Informed Hybrid Reservoir Computingcited by 1
  9. 2025Tailored minimal reservoir computing: on the bidirectional connection between nonlinearities in the reservoir and in datacited by 0
  10. 2026Flow map learning in nonlinear vector autoregressive models: influence of the feature-library structure on the training errorcited by 0
  11. 2026Causal Local States: Scalable Simultaneous Causal Network Inference and Forecasting for Dynamical Systemscited by 0