# A Systematic Exploration of Reservoir Computing for Forecasting Complex Spatiotemporal Dynamics

arXiv: https://arxiv.org/abs/2201.08910 · HTML: https://mlsanity.com/paper/2201.08910/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jan 2022.

## Built on by (most cited first, 30 of 30)

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- [SMT 2.0: A Surrogate Modeling Toolbox with a focus on Hierarchical and Mixed Variables Gaussian Processes](https://mlsanity.com/paper/2305.13998/) (2023)
- [Learning Spatiotemporal Chaos Using Next-Generation Reservoir Computing](https://mlsanity.com/paper/2203.13294/) (2022)
- [True Zero-Shot Inference of Dynamical Systems Preserving Long-Term Statistics](https://mlsanity.com/paper/2505.13192/) (2025)
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- [Learning Interpretable Hierarchical Dynamical Systems Models from Time Series Data](https://mlsanity.com/paper/2410.04814/) (2024)
- [Integrating Multimodal Data for Joint Generative Modeling of Complex Dynamics](https://mlsanity.com/paper/2212.07892/) (2022)
- [Attractor reconstruction with reservoir computers: The effect of the reservoir's conditional Lyapunov exponents on faithful attractor reconstruction](https://mlsanity.com/paper/2401.00885/) (2023)
- [Learning dynamical systems with hit-and-run random feature maps](https://mlsanity.com/paper/2501.06661/) (2025)
- [Constraining Chaos: Enforcing dynamical invariants in the training of recurrent neural networks](https://mlsanity.com/paper/2304.12865/) (2023)
- [4D-Var using Hessian approximation and backpropagation applied to automatically-differentiable numerical and machine learning models](https://mlsanity.com/paper/2408.02767/) (2024)
- [The Seismic Wavefield Common Task Framework](https://mlsanity.com/paper/2512.19927/) (2025)
- [Robust quantum reservoir computers for forecasting chaotic dynamics: generalized synchronization and stability](https://mlsanity.com/paper/2506.22335/) (2025)
- [Continuous-Time Piecewise-Linear Recurrent Neural Networks](https://mlsanity.com/paper/2602.15649/) (2026)
- [Position: A Dynamical Systems Perspective is Needed to Advance Time Series Modeling](https://mlsanity.com/paper/2602.16864/) (2026)
- [Temporal Subsampling Diminishes Small Spatial Scales in Recurrent Neural Network Emulators of Geophysical Turbulence](https://mlsanity.com/paper/2305.00100/) (2023)
- [Dynamic Reservoir Computing with Physical Neuromorphic Networks](https://mlsanity.com/paper/2505.16813/) (2025)
- [Tailored Forecasting from Short Time Series via Meta-learning](https://mlsanity.com/paper/2501.16325/) (2025)
- [Learning Beyond Experience: Generalizing to Unseen State Space with Reservoir Computing](https://mlsanity.com/paper/2506.05292/) (2025)
- [Minimal Deterministic Echo State Networks Outperform Random Reservoirs in Learning Chaotic Dynamics](https://mlsanity.com/paper/2507.06050/) (2025)
- [Ultra-Early Prediction of Tipping Points: Integrating Dynamical Measures with Reservoir Computing](https://mlsanity.com/paper/2603.14944/) (2026)
- [Oscillations enhance time-series prediction in reservoir computing with feedback](https://mlsanity.com/paper/2406.02867/) (2024)
- [Learning Chaotic Dynamics with Neuromorphic Network Dynamics](https://mlsanity.com/paper/2506.10773/) (2025)
- [Machine-Precision Prediction of Low-Dimensional Chaotic Systems from Noise-Free Data](https://mlsanity.com/paper/2507.09652/) (2025)
- [Using Echo-State Networks to Reproduce Rare Events in Chaotic Systems](https://mlsanity.com/paper/2505.16208/) (2025)
- [A tensor network approach for chaotic time series prediction](https://mlsanity.com/paper/2505.17740/) (2025)
- [Sequential Reservoir Computing for Efficient High-Dimensional Spatiotemporal Forecasting](https://mlsanity.com/paper/2601.00172/) (2026)
- [AugRelNet: Relation-Augmented Dynamics for Structure Discovery and Forecasting from Limited Data](https://mlsanity.com/paper/2606.11251/) (2026)
- [Topological Out-of-Domain Generalization in Dynamical Systems Reconstruction](https://mlsanity.com/paper/2606.22969/) (2026)
- [A Minimal Interpretable Architecture for Zero-Shot Reconstruction of Dynamical Systems](https://mlsanity.com/paper/2607.14937/) (2026)

## Abstract (arXiv)

A reservoir computer (RC) is a type of simplified recurrent neural network architecture that has demonstrated success in the prediction of spatiotemporally chaotic dynamical systems. A further advantage of RC is that it reproduces intrinsic dynamical quantities essential for its incorporation into numerical forecasting routines such as the ensemble Kalman filter -- used in numerical weather prediction to compensate for sparse and noisy data. We explore here the architecture and design choices for a "best in class" RC for a number of characteristic dynamical systems, and then show the application of these choices in scaling up to larger models using localization. Our analysis points to the importance of large scale parameter optimization. We also note in particular the importance of including input bias in the RC design, which has a significant impact on the forecast skill of the trained RC model. In our tests, the the use of a nonlinear readout operator does not affect the forecast time or the stability of the forecast. The effects of the reservoir dimension, spinup time, amount of training data, normalization, noise, and the RC time step are also investigated. While we are not aware of a generally accepted best reported mean forecast time for different models in the literature, we report over a factor of 2 increase in the mean forecast time compared to the best performing RC model of Vlachas et.al (2020) for the 40 dimensional spatiotemporally chaotic Lorenz 1996 dynamics, and we are able to accomplish this using a smaller reservoir size.