EchoStateNetwork

Echo state networks / reservoir computing in pure numpy. One class, EchoStateNetwork: ridge-regression training with chaotic recycle validation (contiguous runs or ragged dwell segments), parametric inputs, optional Bayesian hyperparameter search (scikit-optimize), closed-loop prediction, and Jacobians for data assimilation. For spatially extended systems, the parallel layout (patch_size, halo, periodic) runs one reservoir per patch of neighbouring sites (Pathak et al. 2018), with shared matrices and a position for every reservoir row, which covariance localization requires; see the parallel ESN page.

This is the single shared reservoir core behind qlrom (quantized-local ESN families) and romda (real-time ESN forecasting and bias-aware data assimilation).

Documentation: https://andreanovoa.github.io/EchoStateNetwork/

Tutorials

• tutorials/01_echo_state_network.ipynb — train an ESN on the Lorenz 63 system, with full and partial observability.
• tutorials/02_parametric_esn.ipynb — one reservoir conditioned on a physical parameter, forecasting at unseen parameter values.
• tutorials/05_parallel_esn_kuramoto_sivashinsky.ipynb — global, parallel (shared matrices) and local (independent patches) networks on the Kuramoto–Sivashinsky equation.
• tutorials/06_esn_architectures.ipynb — drawings of the architectures that the constructor keywords build, a gallery and an interactive explorer (ipywidgets).

Install

pip install echostatenetwork          # core (numpy/scipy/matplotlib)
pip install "echostatenetwork[opt]"   # + scikit-optimize for Bayesian hyperparameter search
pip install -e ".[dev]"               # development

Quickstart

import numpy as np
from echostatenetwork import EchoStateNetwork

y = my_time_series                       # (Nt, N_dim)
esn = EchoStateNetwork(y, dt=0.01, N_units=200, t_train=40.0, t_val=4.0)
esn.train([y])
u_wash, r = ...                          # see docstrings: washout then closed loop

Citation

If this package contributes to your work, please cite the software archive on Zenodo:

@software{novoa_echostatenetwork,
  author = {Nóvoa, Andrea},
  title = {echostatenetwork: echo state networks in pure numpy},
  publisher = {Zenodo},
  doi = {10.5281/zenodo.23266679},
  url = {https://doi.org/10.5281/zenodo.23266679},
}

and the paper that introduced chaotic recycle validation, which train() employs by default:

@article{racca2021robust,
  author = {Racca, Alberto and Magri, Luca},
  title = {Robust optimization and validation of echo state networks for learning chaotic dynamics},
  journal = {Neural Networks},
  volume = {142},
  pages = {252--268},
  year = {2021},
  doi = {10.1016/j.neunet.2021.05.004},
  url = {https://doi.org/10.1016/j.neunet.2021.05.004},
}

Acknowledgements

This repository is based on alberacca/Echo-State-Networks, the reference implementation of the recycle-validation echo state network by Racca & Magri (2021). The parallel layout follows Pathak et al. (2018) and Vlachas et al. (2020).

• Pathak, J., Hunt, B., Girvan, M., Lu, Z., & Ott, E. (2018). Model-free prediction of large spatiotemporally chaotic systems from data: a reservoir computing approach. Physical Review Letters, 120, 024102. doi:10.1103/PhysRevLett.120.024102
• Vlachas, P. R., Pathak, J., Hunt, B. R., Sapsis, T. P., Girvan, M., Ott, E., & Koumoutsakos, P. (2020). Backpropagation algorithms and reservoir computing in recurrent neural networks for the forecasting of complex spatiotemporal dynamics. Neural Networks, 126, 191-217. doi:10.1016/j.neunet.2020.02.016