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.
- torchid: 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 modelWH2009_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.
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
If you find this project useful, we encourage you to
- Star this repository ⭐
- 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}
}