SINDy vs Hard Nonlinearities and Hidden Dynamics: a Benchmarking Study

This is the code repository for the article "SINDy vs Hard Nonlinearities and Hidden Dynamics: a Benchmarking Study" (Aurelio Raffa Ugolini¹, Valentina Breschi², Andrea Manzoni³, Mara Tanelli¹), available on arXiv

Introduction

In this work we analyze the effectiveness of the Sparse Identification of Nonlinear Dynamics (SINDy) technique on three benchmark datasets for nonlinear identification, to provide a better understanding of its suitability when tackling real dynamical systems. While SINDy can be an appealing strategy for pursuing physics-based learning, our analysis highlights difficulties in dealing with unobserved states and non-smooth dynamics. Due to the ubiquity of these features in real systems in general, and control applications in particular, we complement our analysis with hands-on approaches to tackle these issues in order to exploit SINDy also in these challenging contexts.

Installation

Once you download or clone the repository, you can configure the environment via Pipenv through the provided Pipfile and Pipfile.lock.

Note: the lock file has been generated on a macOS machine, so you might need to delete it if you are running on a different OS. Pipenv will take care of the generation of a new Pipfile.lock and proceed with the installation.

Usage

Each experiment detailed in the paper is implemented in a self-contained script under src/experiments. To execute the experiments, navigate to the src/experiments folder and run the script via

python <EXPERIMENT_NAME>.py

where <EXPERIMENT_NAME> is replaced by:

• pick_and_place for the Pick and Place Machine experiment;
• bouc_wen for the Bouc-Wen hysteresis model experiment;
• cascaded_tanks for the Cascaded Tanks dataset.

Notice that the data have already been provided as part of the repository (under the data directory), except for the pick_and_place whose data is not public.

Bug reporting, inquiries, and more

Please feel free to contact the corresponding author, Aurelio Raffa for issues with the code or other inquiries.

Footnotes

1. Dip. di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Via G. Ponzio 34/5 - 20133 Milano, Italy. ↩ ↩²

2. Dept. of Electrical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands. ↩

3. Dip. di Matematica, Politecnico di Milano, P.zza Leonardo da Vinci 32- 20133 Milano, Italy. ↩