ReservoirComputing.jl

ReservoirComputing.jl is a versatile and user-friendly Julia package designed for the implementation of Reservoir Computing models, such as Echo State Networks (ESNs). Reservoir Computing expands the input data into a higher-dimensional space, leveraging regression techniques for effective model training. This approach can be thought as a kernel method with an explicit kernel trick.

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 liquid state machines, the others are in-depth review papers that should cover all the needed information. For the majority of the algorithms implemented in this library we cited in the documentation the original work introducing them. If you ever are in doubt about a method or a function just type ? function in the Julia REPL to read the relevant notes.

Jaeger, Herbert: The “echo state” approach to analyzing 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.

Performance tip

For faster computations on the CPU it is suggested to add using MKL to the script. For clarity's sake this library will not be indicated under every example in the documentation.

Lux's states vs reservoir computing states

ReservoirComputing.jl builds on Lux.jl. As such, it inherits the model’s states st juggling and naming. This contrasts with the naming of the internal expansions of the input data, which in reservoir computing literature are also known as states. Since we cannot avoid using the same name for two different things, we tried to make it as explicit as possible in the documentation when we refer to one or the other. If you feel that this is causing confusion in some places, please open an issue!

Installation

To install ReservoirComputing.jl, ensure you have Julia version 1.10 or higher. Follow these steps:

Open the Julia command line.
Enter the Pkg REPL mode by pressing ].
Type add ReservoirComputing and press Enter.

Alternatively, do:

using Pkg
Pkg.add("ReservoirComputing")

For a more customized installation or to contribute to the package, consider cloning the repository:

using Pkg
Pkg.clone("https://github.com/SciML/ReservoirComputing.jl.git")

or dev the package.

Features Overview

Base layers for reservoir computing model construction. Main layers provide high level reservoir computing building blocks, such as ReservoirComputer and ReservoirChain. Additional, lower level layers provide the building blocks for custom reservoir computers, such as LinearReadout, Collect, ESNCell, DelayLayer, NonlinearFeaturesLayer, and more
Fully built models:
- Echo state networks ESN
- Deep echo state networks DeepESN
- Echo state networks with delayed states DelayESN
- Hybrid echo state networks HybridESN
15+ reservoir initializers and 5+ input layer initializers
5+ reservoir states modification algorithms
Sparse matrix computation through SparseArrays.jl
Multiple training algorithms via LIBSVM.jl and MLJLinearModels.jl

Contributing

Contributions to ReservoirComputing.jl are highly encouraged and appreciated. Whether it's through implementing new RC model variations, enhancing documentation, adding examples, or any improvement, your contribution is valuable. We welcome posts of relevant papers or ideas in the issues section. For deeper insights into the library's functionality, the API section in the documentation is a great resource. For any queries not suited for issues, please reach out to the lead developers via Slack or email.

Citing

If you use ReservoirComputing.jl in your work, we kindly ask you to cite it. Here is the BibTeX entry for your convenience:

@article{martinuzzi2022reservoircomputing,
  author  = {Francesco Martinuzzi and Chris Rackauckas and Anas Abdelrehim and Miguel D. Mahecha and Karin Mora},
  title   = {ReservoirComputing.jl: An Efficient and Modular Library for Reservoir Computing Models},
  journal = {Journal of Machine Learning Research},
  year    = {2022},
  volume  = {23},
  number  = {288},
  pages   = {1--8},
  url     = {http://jmlr.org/papers/v23/22-0611.html}
}

Reproducibility

The documentation of this SciML package was built using these direct dependencies,

Status `/var/lib/buildkite-agent/builds/gpuci-6/julialang/reservoircomputing-dot-jl/docs/Project.toml`
  [878138dc] CellularAutomata v0.0.6
  [e30172f5] Documenter v1.16.1
  [daee34ce] DocumenterCitations v1.4.1
  [d12716ef] DocumenterInterLinks v1.1.0
  [1dea7af3] OrdinaryDiffEq v6.103.0
  [91a5bcdd] Plots v1.41.2
  [7c2d2b1e] ReservoirComputing v0.12.3 `/var/lib/buildkite-agent/builds/gpuci-6/julialang/reservoircomputing-dot-jl`
  [2913bbd2] StatsBase v0.34.9
  [37e2e46d] LinearAlgebra v1.12.0
  [9a3f8284] Random v1.11.0

and using this machine and Julia version.

Julia Version 1.12.2
Commit ca9b6662be4 (2025-11-20 16:25 UTC)
Build Info:
  Official https://julialang.org release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 48 × AMD EPYC 7402 24-Core Processor
  WORD_SIZE: 64
  LLVM: libLLVM-18.1.7 (ORCJIT, znver2)
  GC: Built with stock GC
Threads: 1 default, 1 interactive, 1 GC (on 2 virtual cores)
Environment:
  JULIA_CPU_THREADS = 2
  JULIA_DEPOT_PATH = /root/.cache/julia-buildkite-plugin/depots/01852978-cea0-41b9-93ac-ff3dc03e5dc5
  LD_LIBRARY_PATH = /usr/local/nvidia/lib:/usr/local/nvidia/lib64:/usr/local/cuda/lib64
  JULIA_PKG_SERVER =

A more complete overview of all dependencies and their versions is also provided.

Status `/var/lib/buildkite-agent/builds/gpuci-6/julialang/reservoircomputing-dot-jl/docs/Manifest.toml`
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  [b77e0a4c] InteractiveUtils v1.11.0
  [ac6e5ff7] JuliaSyntaxHighlighting v1.12.0
  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.12.0
  [56ddb016] Logging v1.11.0
  [d6f4376e] Markdown v1.11.0
  [a63ad114] Mmap v1.11.0
  [ca575930] NetworkOptions v1.3.0
  [44cfe95a] Pkg v1.12.0
  [de0858da] Printf v1.11.0
  [3fa0cd96] REPL v1.11.0
  [9a3f8284] Random v1.11.0
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.12.0
  [f489334b] StyledStrings v1.11.0
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test v1.11.0
  [cf7118a7] UUIDs v1.11.0
  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.3.0+1
  [deac9b47] LibCURL_jll v8.15.0+0
  [e37daf67] LibGit2_jll v1.9.0+0
  [29816b5a] LibSSH2_jll v1.11.3+1
  [14a3606d] MozillaCACerts_jll v2025.5.20
  [4536629a] OpenBLAS_jll v0.3.29+0
  [05823500] OpenLibm_jll v0.8.7+0
  [458c3c95] OpenSSL_jll v3.5.4+0
  [efcefdf7] PCRE2_jll v10.44.0+1
  [bea87d4a] SuiteSparse_jll v7.8.3+2
  [83775a58] Zlib_jll v1.3.1+2
  [8e850b90] libblastrampoline_jll v5.15.0+0
  [8e850ede] nghttp2_jll v1.64.0+1
  [3f19e933] p7zip_jll v17.7.0+0
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`

You can also download the manifest file and the project file.