dynoNet: A neural network architecture for learning dynamical systems

This repository contains the Python code to reproduce the results of the paper dynoNet: A neural network architecture for learning dynamical systems by Marco Forgione and Dario Piga.

In this work, we introduce the linear dynamical operator as a differentiable layer compatible with back-propagation-based training. The operator is parametrized as a rational transfer function and thus can represent an infinite impulse response (IIR) filtering operation, as opposed to the Convolutional layer of 1D-CNNs that is equivalent to finite impulse response (FIR) filtering.

In the dynoNet architecture, linear dynamical operators are combined with static (i.e., memoryless) non-linearities which can be either elementary activation functions applied channel-wise; fully connected feed-forward neural networks; or other differentiable operators.

A 15-min presentation about dynoNet is available here.

Folders:

• dynonet: PyTorch implementation of the linear dynamical operator (aka G-block in the paper) used in dynoNet
• examples: examples using dynoNet for system identification
• util: definition of metrics R-square, RMSE, fit index
• doc: paper & slides

Three examples discussed in the paper are:

• WH2009: A circuit with Wiener-Hammerstein behavior. Experimental dataset from http://www.nonlinearbenchmark.org
• BW: Bouc-Wen. A nonlinear dynamical system describing hysteretic effects in mechanical engineering. Experimental dataset from http://www.nonlinearbenchmark.org
• EMPS: A controlled prismatic joint (Electro Mechanical Positioning System). Experimental dataset from http://www.nonlinearbenchmark.org

For the WH2009 example, the main scripts are:

• WH2009_train.py: Training of the dynoNet model
• WH2009_test.py: Evaluation of the dynoNet model on the test dataset, computation of metrics.

Similar scripts are provided for the other examples.

NOTE: the original data sets are not included in this project. They have to be manually downloaded from http://www.nonlinearbenchmark.org and copied in the data sub-folder of the example.

Software requirements:

Simulations were performed on a Python 3.7 conda environment with

• numpy
• scipy
• matplotlib
• pandas
• pytorch (version 1.4)

These dependencies may be installed through the commands:

conda install numpy scipy pandas matplotlib
conda install pytorch torchvision cudatoolkit=10.2 -c pytorch

Local installation:

From PyPI

Type in terminal:

pip install dynonet

This will install the latest stable version packaged on PyPI: https://pypi.org/project/dynonet/

From a local copy of this repository

Navigate to a local copy of this repository, where setup.py and setup.cfg are located. Then, type in terminal:

pip install -e .

Citing

If you find this project useful, we encourage you to

• Star this repository :star:
• Cite the paper

@article{forgione2021dyno,
  title={\textit{dyno{N}et}: A neural network architecture for learning dynamical systems},
  author={Forgione, M. and Piga, D.},
  journal={International Journal of Adaptive Control and Signal Processing},
  volume={35},
  number={4},
  pages={612--626},
  year={2021},
  publisher={Wiley}
}