Python library for Reservoir Computing using Echo State Networks
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easyesn is a library for recurrent neural networks using echo state networks (ESNs, also called reservoir computing) with a high level easy to use API that is closely oriented towards sklearn. It aims to make the use of ESN as easy as possible, by providing algorithms for automatic gradient based hyperparameter tuning (of ridge regression penalty, spectral radius, leaking rate and feedback scaling), as well as transient time estimation. Furtheremore, it incorporates the ability to use spatio temporal ESNs for prediction and classification of geometrically extended input signals.

easyesn can either use the CPU or make use of the GPU thanks to cupy. At the moment the use of the CPU is recommended though!

This project is based on research results for the gradient based hyperparameter optimization and transient time estimation of Luca Thiede and the spatio temporal prediction and classification techniques of Roland Zimmermann.

Getting started


The easyesn library is built using python 3. You cannot use it in a python 2.x environment. The recommended way to install easyesn at the moment is via pip. Nevertheless, you can also install easyesn on your own without pip.


You can install easyesn via pip by executing

pip install easyesn

from a valid python 3.x environment, which will automatically install easyesn and its dependencies.


To install the library without pip, there are four steps you have to perform:

  1. Go to the pypi page of easyesn and download the latest version as a *.tar.gz archive.
  2. Extract the archive.
  3. Open your command line/terminal and cd into the directory containing the
  4. Execute python install to start the installation.

First steps

As already mentioned, the API is very similar to the one of sklearn, which makes it as easy as possible for beginners. For every task there is a specialized module, e.g. ClassificationESN for the classification of input signals, PredictionESN for the prediction or generation (that is a several step ahead prediction by always feeding the previous prediction back in), RegressionESN for mapping a signal to a real number, or SpatioTemporalESN for the prediction of geometrically extended input signals (for example the electric excitation on the heart surface or video frames).

Import the module typing

from easyesn import PredictionESN

Now simply fit the esn using, y_train, transientTime=100, verbose=1)

and predict by using

y_test_pred = esn.predict(x_test, transientTime=100, verbose=1)

For automatic hyperparamter optimization import

from easyesn.optimizers import GradientOptimizer
from easyesn.optimizers import GridSearchOptimizer

Next create a new object

esn = PredictionESN(n_input=1, n_output=1, n_reservoir=500, leakingRate=0.2, spectralRadius=0.2, regressionParameters=[1e-2])

whith a penalty 1e-2 for the ridge regression. To optimize the hyperparameter also create an optimizer object

opt = GradientOptimizer(esn, learningRate=0.001)

and use it with

validationLosses, fitLosses, inputScalings, spectralRadiuses, leakingRates, learningRates = opt.optimizeParameterForTrainError(inputDataTraining, outputDataTraining, inputDataValidation, outputDataValidation, epochs=150, transientTime=100)
validationLosses, fitLosses, penalties = opt.optimizePenalty(inputDataTraining, outputDataTraining, inputDataValidation, outputDataValidation, epochs=150, transientTime=100)

More extensive examples can be found in the examples directory.


As already mentioned in the beginning, easyesn can be used either on the CPU or on the GPU. To achieve this, all low level calculations are outsourced into a backend (similiar to the backend technology of keras). To change the backend to another backend named backendName, there are currently two ways:

  1. Modify the settings file, stored at ~/.easyesn/easyesn.json to contain to look like this:

        "backend": "backendName"

    and use easyesn without any further modification inside your code.

  2. Set the EASYESN_BACKEND environment variable to backendName and use easyesn without any further modification inside your code.

At the moment, these are supported backend names:

backend name backend type
numpy numpy (CPU)
np numpy (CPU)
cupy cupy (GPU)
cp cupy (GPU)




At the moment the easyesn library covers not only all basic features of reservoir computing but also some new, state of the art methods for its application. Nevertheless, there are still some more things which should be implemented in future versions. In the following, these feature requests and ideas are listed together which their progress:

  • Ensemble ESNs (25%)
  • Adding support for deep learning methods as the output method (still open)
  • Improved GPU computing performance (still open)