# Bayesian optimization of hyper-parameters in reservoir computing

arXiv: https://arxiv.org/abs/1611.05193 · HTML: https://mlsanity.com/paper/1611.05193/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Nov 2016.

## Built on by (most cited first, 13 of 13)

- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Robust Optimization and Validation of Echo State Networks for learning chaotic dynamics](https://mlsanity.com/paper/2103.03174/) (2021)
- [Learning noise-induced transitions by multi-scaling reservoir computing](https://mlsanity.com/paper/2309.05413/) (2023)
- [Efficient Optimisation of Physical Reservoir Computers using only a Delayed Input](https://mlsanity.com/paper/2401.14371/) (2024)
- [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)
- [Tri-Learn Graph Fusion Network for Attributed Graph Clustering](https://mlsanity.com/paper/2507.13620/) (2025)
- [Forecasting Crude Oil Prices Using Reservoir Computing Models](https://mlsanity.com/paper/2306.03052/) (2023)
- [Tree-based Learning for High-Fidelity Prediction of Chaos](https://mlsanity.com/paper/2403.13836/) (2024)
- [Adaptive control of recurrent neural networks using conceptors](https://mlsanity.com/paper/2405.07236/) (2024)
- [Boosting Reservoir Computing with Brain-inspired Adaptive Dynamics](https://mlsanity.com/paper/2504.12480/) (2025)
- [Empirical Investigation into Configuring Echo State Networks for Representative Benchmark Problem Domains](https://mlsanity.com/paper/2508.10887/) (2025)
- [Inference of Unknown Dynamical Components Using Next Generation Reservoir Computing: From Chaotic Systems to Climate Data](https://mlsanity.com/paper/2609.24754/) (2026)

## Abstract (arXiv)

We describe a method for searching the optimal hyper-parameters in reservoir computing, which consists of a Gaussian process with Bayesian optimization. It provides an alternative to other frequently used optimization methods such as grid, random, or manual search. In addition to a set of optimal hyper-parameters, the method also provides a probability distribution of the cost function as a function of the hyper-parameters. We apply this method to two types of reservoirs: nonlinear delay nodes and echo state networks. It shows excellent performance on all considered benchmarks, either matching or significantly surpassing results found in the literature. In general, the algorithm achieves optimal results in fewer iterations when compared to other optimization methods. We have optimized up to six hyper-parameters simultaneously, which would have been infeasible using, e.g., grid search. Due to its automated nature, this method significantly reduces the need for expert knowledge when optimizing the hyper-parameters in reservoir computing. Existing software libraries for Bayesian optimization, such as Spearmint, make the implementation of the algorithm straightforward. A fork of the Spearmint framework along with a tutorial on how to use it in practice is available at https://bitbucket.org/uhasseltmachinelearning/spearmint/