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We provide an introduction to infinite-dimensional port-Hamiltonian systems. As this research field is quite rich, we restrict ourselves to the class of infinite-dimensional linear port-Hamiltonian systems on a one-dimensional spatial…

Analysis of PDEs · Mathematics 2023-08-04 Birgit Jacob , Hans Zwart

This paper presents a structure-preserving model reduction approach applicable to large-scale, nonlinear port-Hamiltonian systems. Structure preservation in the reduction step ensures the retention of port-Hamiltonian structure which, in…

Numerical Analysis · Mathematics 2016-01-05 Saifon Chaturantabut , Chris Beattie , Serkan Gugercin

In this paper we propose a novel approach to discretize linear port-Hamiltonian systems while preserving the underlying structure. We present a finite element exterior calculus formulation that is able to mimetically represent conservation…

Numerical Analysis · Mathematics 2022-10-19 Andrea Brugnoli , Ramy Rashad , Stefano Stramigioli

We investigate discretization strategies for a recently introduced class of energy-based models. The model class encompasses classical port-Hamiltonian systems, generalized gradient flows, and certain systems with algebraic constraints. Our…

Numerical Analysis · Mathematics 2026-05-29 Robert Altmann , Attila Karsai , Philipp Schulze

We propose a discretization of vector fields that are Hamiltonian up to multiplication by a positive function on the phase space that may be interpreted as a time reparametrization. We prove that our method is structure preserving in the…

Numerical Analysis · Mathematics 2020-08-18 Luis C. García-Naranjo , Mats Vermeeren

In this paper we introduce discrete gradient methods to discretize irreversible port-Hamiltonian systems showing that the main qualitative properties of the continuous system are preserved using this kind discretizations methods.

Numerical Analysis · Mathematics 2023-03-15 Alexandre Anahory Simoes , David Martín de Diego , Bernhard Maschke

The port-Hamiltonian framework is a structure-preserving modeling approach that preserves key physical properties such as energy conservation and dissipation. When subsystems are modeled as port-Hamiltonian systems (pHS) with linearly…

Dynamical Systems · Mathematics 2025-11-26 Matthias Ehrhardt , Michael Günther , Daniel Ševčovič

In this paper we present a novel approach to the geometric formulation of solid and fluid mechanics within the port-Hamiltonian framework, which extends the standard Hamiltonian formulation to non-conservative and open dynamical systems.…

Mathematical Physics · Physics 2024-04-19 Ramy Rashad , Stefano Stramigioli

We introduce the geometric structure underlying the port-Hamiltonian models for distributed parameter systems exhibiting moving material domains.

Analysis of PDEs · Mathematics 2022-03-14 Federico Califano , Ramy Rashad , Frederic P. Schuller , Stefano Stramigioli

This paper investigates the problem of data-driven modeling of port-Hamiltonian systems while preserving their intrinsic Hamiltonian structure and stability properties. We propose a novel neural-network-based port-Hamiltonian modeling…

Systems and Control · Electrical Eng. & Systems 2026-04-16 Binh Nguyen , Nam T. Nguyen , Truong X. Nghiem

We consider infinite dimensional port-Hamiltonian systems. Based on a power balance relation we introduce the port-Hamiltonian system representation where we pay attention to two different scenarios, namely the non-differential operator…

Optimization and Control · Mathematics 2013-08-07 Markus Schöberl , Andreas Siuka

We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general…

Numerical Analysis · Mathematics 2020-09-30 Andrea Brugnoli , Ghislain Haine , Anass Serhani , Xavier Vasseur

This article presents a systematic methodology for modeling a class of flexible multidimensional mechanical structures defined by linear elastic relations that directly allows to obtain their infinite-dimensional port-Hamiltonian…

Dynamical Systems · Mathematics 2023-11-08 Cristobal Ponce , Yongxin Wu , Yann Le Gorrec , Hector Ramirez

A broad class of nonlinear acoustic wave models possess a Hamiltonian structure in their dissipation-free limit and a gradient flow structure for their dissipative dynamics. This structure may be exploited to design numerical methods which…

Numerical Analysis · Mathematics 2024-07-23 William Barham , Philip J. Morrison

This work extends previous 1D irreversible port-Hamiltonian system (IPHS) formulations to boundary-controlled ND distributed parameter systems describing conduction-diffusion fluid phenomena. Within a unified and thermodynamically…

Systems and Control · Electrical Eng. & Systems 2026-03-13 Luis Mora , Yann Le Gorrec , Hector Ramirez , Denis Matignon

A simple Hamiltonian modeling framework for general models in nonlinear optics is given. This framework is specialized to describe the Hamiltonian structure of electromagnetic phenomena in cubicly nonlinear optical media. The model has a…

Computational Physics · Physics 2024-09-10 William Barham , Yaman Güçlü , Philip J. Morrison , Eric Sonnendrücker

For a general class of nonlinear port-Hamiltonian systems we develop a high-order time discretization scheme with certain structure preservation properties. The finite or infinite-dimensional system under consideration possesses a…

Numerical Analysis · Mathematics 2024-07-23 Jan Giesselmann , Attila Karsai , Tabea Tscherpel

Stokes-Dirac structures are infinite-dimensional Dirac structures defined in terms of differential forms on a smooth manifold with boundary. These Dirac structures lay down a geometric framework for the formulation of Hamiltonian systems…

Differential Geometry · Mathematics 2012-06-19 Marko Seslija , Arjan van der Schaft , Jacquelien M. A. Scherpen

The modeling framework of port-Hamiltonian descriptor systems and their use in numerical simulation and control are discussed. The structure is ideal for automated network-based modeling since it is invariant under power-conserving…

Dynamical Systems · Mathematics 2022-01-19 Volker Mehrmann , Benjamin Unger

A well-specified parametrization for single-input/single-output (SISO) linear port-Hamiltonian systems amenable to structure-preserving supervised learning is provided. The construction is based on controllable and observable normal form…

Dynamical Systems · Mathematics 2023-03-07 Juan-Pablo Ortega , Daiying Yin