mlsanityData to 14 Oct 2026

Attractor reconstruction with reservoir computers: The effect of the reservoir's conditional Lyapunov exponents on faithful attractor reconstruction

arXiv 2401.00885 ↗First posted 30 Dec 2023cs.LG nlin.CDcited by 9

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Abstract (arXiv)

Reservoir computing is a machine learning framework that has been shown to be able to replicate the chaotic attractor, including the fractal dimension and the entire Lyapunov spectrum, of the dynamical system on which it is trained. We quantitatively relate the generalized synchronization dynamics of a driven reservoir during the training stage to the performance of the trained reservoir computer at the attractor reconstruction task. We show that, in order to obtain successful attractor reconstruction and Lyapunov spectrum estimation, the largest conditional Lyapunov exponent of the driven reservoir must be significantly more negative than the most negative Lyapunov exponent of the target system. We also find that the maximal conditional Lyapunov exponent of the reservoir depends strongly on the spectral radius of the reservoir adjacency matrix, and therefore, for attractor reconstruction and Lyapunov spectrum estimation, small spectral radius reservoir computers perform better in general. Our arguments are supported by numerical examples on well-known chaotic systems.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 18 of its 69 references that are in the map. First posted on arXiv 30 Dec 2023.

Builds on

18 of 69 references.

References · 18

  1. 2019Model-free prediction of spatiotemporal dynamical systems with recurrent neural networks: Role of network spectral radiuscited by 34
  2. 2022Using Machine Learning to Anticipate Tipping Points and Extrapolate to Post-Tipping Dynamics of Non-Stationary Dynamical Systemscited by 33
  3. 2022A Systematic Exploration of Reservoir Computing for Forecasting Complex Spatiotemporal Dynamicscited by 30
  4. 2020Multifunctionality in a Reservoir Computercited by 21
  5. 2021Model-free inference of unseen attractors: Reconstructing phase space features from a single noisy trajectory using reservoir computingcited by 21
  6. 2018Using a reservoir computer to learn chaotic attractors, with applications to chaos synchronisation and cryptographycited by 16
  7. 2018Machine-learning inference of fluid variables from data using reservoir computingcited by 16
  8. 2020Model-Free Control of Dynamical Systems with Deep Reservoir Computingcited by 12
  9. 2022Learning unseen coexisting attractorscited by 12
  10. 2023Seeing double with a multifunctional reservoir computercited by 12
  11. 2019Using Machine Learning to Assess Short Term Causal Dependence and Infer Network Linkscited by 10
  12. 2020Deep Time-Delay Reservoir Computing: Dynamics and Memory Capacitycited by 10
6 more
  1. 2023Embedding Theory of Reservoir Computing and Reducing Reservoir Network Using Time Delayscited by 10
  2. 2020Machine Learning Link Inference of Noisy Delay-coupled Networks with Opto-Electronic Experimental Testscited by 7
  3. 2019Dimension of Reservoir Computerscited by 6
  4. 2021Reservoir Computers with Random and Optimized Time-Shiftscited by 5
  5. 2021Learn one size to infer all: Exploiting translational symmetries in delay-dynamical and spatio-temporal systems using scalable neural networkscited by 3
  6. 2022Time Shifts to Reduce the Size of Reservoir Computerscited by 3

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 3; 2025: 4; 2026: 2.

9 papers.

  1. 2025A Novel Approach for Estimating Largest Lyapunov Exponents in One-Dimensional Chaotic Time Series Using Machine Learningcited by 6
  2. 2025Robust quantum reservoir computers for forecasting chaotic dynamics: generalized synchronization and stabilitycited by 5
  3. 2024Designing Chaotic Attractors: A Semi-supervised Approachcited by 3
  4. 2025Minimal Deterministic Echo State Networks Outperform Random Reservoirs in Learning Chaotic Dynamicscited by 2
  5. 2024Modeling Nonlinear Oscillator Networks Using Physics-Informed Hybrid Reservoir Computingcited by 1
  6. 2024Reconstruction of neuromorphic dynamics from a single scalar time series using variational autoencoder and neural network mapcited by 0
  7. 2025On the dimension of pullback attractors in recurrent neural networkscited by 0
  8. 2026Storage and selection of multiple chaotic attractors in minimal reservoir computerscited by 0
  9. 2026Beyond the Edge of Chaos: Stability-Expressivity Transfer in Reservoir Forecastingcited by 0