ApHIN - Autoencoder-based port-Hamiltonian Identification Networks

A data-driven framework for the identification of latent port-Hamiltonian systems [1].

Reference

The preprint is available on arXiv. If you use this project for academic work, please consider citing it

Johannes Rettberg, Jonas Kneifl, Julius Herb, Patrick Buchfink, Jörg Fehr, and Bernard Haasdonk. 
Data-driven identification of latent port-Hamiltonian systems. Arxiv, 2024.

Abstract

Conventional physics-based modeling techniques involve high effort, e.g.~time and expert knowledge, while data-driven methods often lack interpretability, structure, and sometimes reliability. To mitigate this, we present a data-driven system identification framework that derives models in the port-Hamiltonian (pH) formulation. This formulation is suitable for multi-physical systems while guaranteeing the useful system theoretical properties of passivity and stability.

Our framework combines linear and nonlinear reduction with structured, physics-motivated system identification. In this process, high-dimensional state data obtained from possibly nonlinear systems serves as the input for an autoencoder, which then performs two tasks: (i) nonlinearly transforming and (ii) reducing this data onto a low-dimensional manifold. In the resulting latent space, a pH system is identified by considering the unknown matrix entries as weights of a neural network. The matrices strongly satisfy the pH matrix properties through Cholesky factorizations. In a joint optimization process over the loss term, the pH matrices are adjusted to match the dynamics observed by the data, while defining a linear pH system in the latent space per construction. The learned, low-dimensional pH system can describe even nonlinear systems and is rapidly computable due to its small size.

The method is exemplified by a parametric mass-spring-damper and a nonlinear pendulum example as well as the high-dimensional model of a disc brake with linear thermoelastic behavior.

Features

This repository implements neural networks that identify linear port-Hamiltonian systems from (potentially high-dimensional) data[1].

• Autoencoders (AEs) for dimensionality reduction
• pH layer to identify system matrices that fulfill the definition of a linear pH system
• pHIN: identify a (parametric) low-dimensional port-Hamiltonian system directly
• ApHIN: identify a (parametric) low-dimensional latent port-Hamiltonian system based on coordinate representations found using an autoencoder
• Examples for the identification of linear pH systems from data
  • One-dimensional mass-spring-damper chain
  • Pendulum
  • discbrake model

Installation

You can either clone the repository and install the package locally or install it directly from PyPI.

PyPI

pip install aphin

Local

Clone this repository and install it to your local environment as package using pip:

git clone https://github.com/Institute-Eng-and-Comp-Mechanics-UStgt/ApHIN.git
cd ApHIN

Then you can activate the environment in which you want to install the package, and use pip to perform the installation.

pip install -e .

⚠️ Please note that you need pip version 24.0 to install the repository in editable mode. Either upgrade pip to the latest version or install it without the -e argument

References

[1] Johannes Rettberg, Jonas Kneifl, Julius Herb, Patrick Buchfink, Jörg Fehr, and Bernard Haasdonk. Data-driven identification of latent port-Hamiltonian systems. Arxiv, 2024.

[2] Volker Mehrmann and Benjamin Unger. Control of port-Hamiltonian differential-algebraic systems and applications, 2022.

[3] Kathleen Champion, Bethany Lusch, J. Nathan Kutz, and Steven L. Brunton. Data-driven discovery of coordinates and governing equations. Proceedings of the National Academy of Sciences, 116(45):22445–22451, 2019.