ApHIN - Autoencoder-based port-Hamiltonian Identification Networks (Software Package)

<h3>Software package for data-driven identification of latent port-Hamiltonian systems.</h3>

<h3>Abstract</h3>

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.<br>

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.<br>

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

<h3>Features</h3>

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

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

See <a href="https://institute-eng-and-comp-mechanics-ustgt.github.io/ApHIN/">documentation</a> for more details.