Reservoir Computing is an umbrella term used to describe a family of models such as Echo State Networks (ESNs) and Liquid State Machines (LSMs). The key concept is to expand the input data into a higher dimension and use regression in order to train the model; in some ways Reservoir Computers can be considered similar to kernel methods.

Introductory material

This library assumes some basic knowledge of Reservoir Computing. For a good introduction, we suggest the following papers: the first two are the seminal papers about ESN and LSM, the others are in-depth review papers that should cover all the needed information.

  • Jaeger, Herbert: The “echo state” approach to analysing and training recurrent neural networks-with an erratum note.
  • Maass W, Natschläger T, Markram H: Real-time computing without stable states: a new framework for neural computation based on perturbations.
  • Lukoševičius, Mantas: A practical guide to applying echo state networks." Neural networks: Tricks of the trade.
  • Lukoševičius, Mantas, and Herbert Jaeger: Reservoir computing approaches to recurrent neural network training.

In this package (for the moment) there are the following models:

  • Echo State Networks (ESNs)
  • Support Vector Echo State Machines [1] (SVESMs)
  • Echo State Gaussian Processes [2] (ESGPs)
  • Reservoir Computing with Cellular Automata [3] (RECAs)
  • Reservoir Memory Machine [4] (RMMs)
  • Double Activation Echo State Networks [5] (DAFESNs)

Multiple features are present as well, like the possibility of using a number of different reservoir and input layer architectures, as well as different linear regression methods. For more information on this please refer to the examples.


Since ReservoirComputing is registered in the Julia General Registry, it will suffice to do the following in the Julia REPL:

]add ReservoirComputing


[1]: Shi, Zhiwei, and Min Han. "Support vector echo-state machine for chaotic time-series prediction." IEEE Transactions on Neural Networks 18.2 (2007): 359-372.

[2]: Chatzis, Sotirios P., and Yiannis Demiris. "Echo state Gaussian process." IEEE Transactions on Neural Networks 22.9 (2011): 1435-1445.

[3]: Yilmaz, Ozgur. "Reservoir computing using cellular automata." arXiv preprint arXiv:1410.0162 (2014).

[4]: Paaßen, Benjamin, and Alexander Schulz. "Reservoir memory machines." arXiv preprint arXiv:2003.04793 (2020).

[5]: Lun, Shu-Xian, et al. "A novel model of leaky integrator echo state network for time-series prediction." Neurocomputing 159 (2015): 58-66.