Related papers: Model reduction techniques for linear constant coe…
We develop inductive biases for the machine learning of complex physical systems based on the port-Hamiltonian formalism. To satisfy by construction the principles of thermodynamics in the learned physics (conservation of energy,…
This paper presents a structure-preserving spatial discretization method for distributed parameter port-Hamiltonian systems. The class of considered systems are hyperbolic systems of two conservation laws in arbitrary spatial dimension and…
The anisotropic and heterogeneous $N$-dimensional wave equation, controlled and observed at the boundary, is considered as a port-Hamiltonian system. A recent structure-preserving mixed Galerkin method is applied, leading directly to a…
Many applications, such as optimization, uncertainty quantification and inverse problems, require repeatedly performing simulations of large-dimensional physical systems for different choices of parameters. This can be prohibitively…
In this paper, we develop high-order splitting methods for linear port-Hamiltonian systems, focusing on preserving their intrinsic structure, particularly the dissipation inequality. Port-Hamiltonian systems are characterized by their…
Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks and demonstrate a significant…
Hamiltonian operator inference has been developed in [Sharma, H., Wang, Z., Kramer, B., Physica D: Nonlinear Phenomena, 431, p.133122, 2022] to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. The method…
We give a short overview of advantages and drawbacks of the classical formulation of minimum cost network flow problems and solution techniques, to motivate a reformulation of classical static minimum cost network flow problems as optimal…
We prove a one-to-one correspondence between the geometric formulation of port-Hamiltonian (pH) systems defined by Dirac structures, Lagrange structures, maximal resistive structures, and external ports and a state-space formulation by…
We present a new optimization-based structure-preserving model order reduction (MOR) method for port-Hamiltonian descriptor systems (pH-DAEs) with differentiation index two. Our method is based on a novel parameterization that allows us to…
Mathematical modeling of real-world physical systems requires the consistent combination of a multitude of physical laws and phenomenological models. This challenging task can be greatly simplified by hierarchically decomposing systems into…
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…
This paper presents a port-Hamiltonian formulation of vehicle-manipulator systems (VMS), a broad class of robotic systems including aerial manipulators, underwater manipulators, space robots, and omnidirectional mobile manipulators. Unlike…
This work presents two novel approaches for the symplectic model reduction of high-dimensional Hamiltonian systems using data-driven quadratic manifolds. Classical symplectic model reduction approaches employ linear symplectic subspaces for…
After recalling standard nonlinear port-Hamiltonian systems and their algebraic constraint equations, called here Dirac algebraic constraints, an extended class of port-Hamiltonian systems is introduced. This is based on replacing the…
Learning dynamical systems through purely data-driven methods is challenging as they do not learn the underlying conservation laws that enable them to correctly generalize. Existing port-Hamiltonian neural network methods have recently been…
In this note, we consider port-Hamiltonian structures in numerical optimal control of ordinary differential equations. By introducing a novel class of nonlinear monotone port-Hamiltonian (pH) systems, we show that the primal-dual gradient…
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…
We study the structure-preserving space discretization of port-Hamiltonian (pH) systems defined with differential constitutive relations. Using the concept of Stokes-Lagrange structure to describe these relations, these are reduced to a…
We introduce the geometric structure underlying the port-Hamiltonian models for distributed parameter systems exhibiting moving material domains.