# Forecasting Chaotic Systems with Very Low Connectivity Reservoir Computers

arXiv: https://arxiv.org/abs/1910.00659 · HTML: https://mlsanity.com/paper/1910.00659/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Oct 2019.

## Built on by (most cited first, 30 of 43)

- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Using Machine Learning to Anticipate Tipping Points and Extrapolate to Post-Tipping Dynamics of Non-Stationary Dynamical Systems](https://mlsanity.com/paper/2207.00521/) (2022)
- [Robust Optimization and Validation of Echo State Networks for learning chaotic dynamics](https://mlsanity.com/paper/2103.03174/) (2021)
- [Anticipating synchronization with machine learning](https://mlsanity.com/paper/2103.13358/) (2021)
- [Adaptable Hamiltonian neural networks](https://mlsanity.com/paper/2102.13235/) (2021)
- [Integrating Recurrent Neural Networks with Data Assimilation for Scalable Data-Driven State Estimation](https://mlsanity.com/paper/2109.12269/) (2021)
- [Catch-22s of reservoir computing](https://mlsanity.com/paper/2210.10211/) (2022)
- [Embedding Theory of Reservoir Computing and Reducing Reservoir Network Using Time Delays](https://mlsanity.com/paper/2303.09042/) (2023)
- [Data-driven model discovery with Kolmogorov-Arnold networks](https://mlsanity.com/paper/2409.15167/) (2024)
- [Symmetry-Aware Reservoir Computing](https://mlsanity.com/paper/2102.00310/) (2021)
- [Chaotic attractor reconstruction using small reservoirs -- the influence of topology](https://mlsanity.com/paper/2402.16888/) (2024)
- [Hyperparameter Optimization for Randomized Algorithms: A Case Study on Random Features](https://mlsanity.com/paper/2407.00584/) (2024)
- [Constraining Chaos: Enforcing dynamical invariants in the training of recurrent neural networks](https://mlsanity.com/paper/2304.12865/) (2023)
- [Forecasting trends in food security with real time data](https://mlsanity.com/paper/2312.00626/) (2023)
- [Hybridizing Traditional and Next-Generation Reservoir Computing to Accurately and Efficiently Forecast Dynamical Systems](https://mlsanity.com/paper/2403.18953/) (2024)
- [Controlling nonlinear dynamical systems into arbitrary states using machine learning](https://mlsanity.com/paper/2102.12969/) (2021)
- [Cluster-based Input Weight Initialization for Echo State Networks](https://mlsanity.com/paper/2103.04710/) (2021)
- [Machine-learning parameter tracking with partial state observation](https://mlsanity.com/paper/2311.09142/) (2023)
- [`Next Generation' Reservoir Computing: an Empirical Data-Driven Expression of Dynamical Equations in Time-Stepping Form](https://mlsanity.com/paper/2201.05193/) (2022)
- [Temporal Subsampling Diminishes Small Spatial Scales in Recurrent Neural Network Emulators of Geophysical Turbulence](https://mlsanity.com/paper/2305.00100/) (2023)
- [Learning Hamiltonian dynamics by reservoir computer](https://mlsanity.com/paper/2104.14474/) (2021)
- [Digital twins of nonlinear dynamical systems](https://mlsanity.com/paper/2210.06144/) (2022)
- [Emergence of a stochastic resonance in machine learning](https://mlsanity.com/paper/2211.09955/) (2022)
- [Effect of temporal resolution on the reproduction of chaotic dynamics via reservoir computing](https://mlsanity.com/paper/2302.10761/) (2023)
- [Learning unidirectional coupling using echo-state network](https://mlsanity.com/paper/2303.13562/) (2023)
- [Reservoir Computing with Error Correction: Long-term Behaviors of Stochastic Dynamical Systems](https://mlsanity.com/paper/2305.00669/) (2023)
- [Learning to learn ecosystems from limited data -- a meta-learning approach](https://mlsanity.com/paper/2410.07368/) (2024)
- [Reconstructing dynamics from sparse observations with no training on target system](https://mlsanity.com/paper/2410.21222/) (2024)
- [Minimal Deterministic Echo State Networks Outperform Random Reservoirs in Learning Chaotic Dynamics](https://mlsanity.com/paper/2507.06050/) (2025)
- [Dimensional criterion for forecasting nonlinear systems by reservoir computing](https://mlsanity.com/paper/2202.05159/) (2022)

## 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.