# 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](https://arxiv.org/pdf/2006.02250.pdf) 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](https://www.youtube.com/watch?v=SrrlhGPLBrA&t=55s).
# Folders:
* [dynonet](src/dynonet): PyTorch implementation of the linear dynamical operator (aka G-block in the paper) used in dynoNet
* [examples](examples): examples using dynoNet for system identification
* [util](util): definition of metrics R-square, RMSE, fit index
* [doc](doc): paper & slides
Three [examples](examples) discussed in the paper are:
* [WH2009](examples/WH2009): A circuit with Wiener-Hammerstein behavior. Experimental dataset from http://www.nonlinearbenchmark.org
* [BW](examples/BW): Bouc-Wen. A nonlinear dynamical system describing hysteretic effects in mechanical engineering. Experimental dataset from http://www.nonlinearbenchmark.org
* [EMPS](examples/EMPS): A controlled prismatic joint (Electro Mechanical Positioning System). Experimental dataset from http://www.nonlinearbenchmark.org
For the [WH2009](examples/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](https://onlinelibrary.wiley.com/doi/abs/10.1002/acs.3216)
```
@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}
}
```