Related papers: Discrete gradient methods for irreversible port-Ha…
We express discrete Painlev\'e equations as discrete Hamiltonian systems. The discrete Hamiltonian systems here mean the canonical transformations defined by generating functions. Our construction relies on the classification of the…
In this paper, we consider local and uniform invariance preserving steplength thresholds on a set when a discretization method is applied to a linear or nonlinear dynamical system. For the forward or backward Euler method, the existence of…
Port-Hamiltonian (pH) systems offer a highly structured and energy-based modular framework for control systems. Many pH systems exhibit non-polynomial non-linearities. We consider the problem of immersing such systems into a…
We study the regularization problem for port-Hamiltonian descriptor systems by proportional and/or derivative output feedback. Necessary and sufficient conditions are given, which guarantee that there exist output feedbacks such that the…
The present work is a successor of [Ilchmann, Kirchhoff 2022] on generic controllability and of [Ilchmann, Kirchhoff 2023] on relative generic controllability of linear differential-algebraic equations. We extend the result from general,…
The discretization approximation method commonly used to simulate the dynamics of quantum system coupled to the environment in continuum often suffers from the periodically partial recovery of initial state because of the effect of finite…
In this paper, we propose integrable discretizations of a two-dimensional Hamiltonian system with quartic potentials. Using either the method of separation of variables or the method based on bilinear forms, we construct the corresponding…
A method of integrable discretization of the Liouville type nonlinear partial differential equations is suggested based on integrals. New examples of discrete Liouville type models are presented.
Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…
We study the numerical behaviour of a particle method for gradient flows involving linear and nonlinear diffusion. This method relies on the discretisation of the energy via non-overlapping balls centred at the particles. The resulting…
This paper investigates gradient recovery schemes for data defined on discretized manifolds. The proposed method, parametric polynomial preserving recovery (PPPR), does not require the tangent spaces of the exact manifolds, and they have…
We present high-order variational Lagrangian finite element methods for compressible fluids using a discrete energetic variational approach. Our spatial discretization is mass/momentum/energy conserving and entropy stable. Fully implicit…
Compatible discretizations, such as finite element exterior calculus, provide a discretization framework that respect the cohomological structure of the de Rham complex, which can be used to systematically construct stable mixed finite…
This paper explores numerical methods for solving a convex differentiable semi-infinite program. We introduce a primal-dual gradient method which performs three updates iteratively: a momentum gradient ascend step to update the constraint…
In this contribution, we extend the hybridization framework for the Hodge Laplacian [Awanou et al., Hybridization and postprocessing in finite element exterior calculus, 2023] to port-Hamiltonian systems describing linear wave propagation…
Gradient-based Markov Chain Monte Carlo methods have recently received much attention for sampling discrete distributions, with notable examples such as Norm Constrained Gradient (NCG), Auxiliary Variable Gradient (AVG), and Discrete…
In this paper, we consider the use of discrete gradients for differential-algebraic equations (DAEs) with a conservation/dissipation law. As one of the most popular numerical methods for conservative/dissipative ordinary differential…
Numerical methods that preserve geometric invariants of the system, such as energy, momentum or the symplectic form, are called geometric integrators. Variational integrators are an important class of geometric integrators. The general idea…
Modeling the dynamics of flexible objects has become an emerging topic in the community as these objects become more present in many applications, e.g., soft robotics. Due to the properties of flexible materials, the movements of soft…
Computing gradients of a cost function is central to design-based optimization and machine learning algorithms. Equilibrium propagation provides an exact method to compute gradients in hardware by exploiting the inherent physical laws. The…