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

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 package 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 fullfill 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 See documentation for more details.