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Related papers: Energy-Based Modeling and Structure-Preserving Dis…

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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 introduce an energy-based model, which seems especially suited for constrained systems. The proposed model provides an alternative to the popular port-Hamiltonian framework and exhibits similar properties such as energy dissipation as…

Numerical Analysis · Mathematics 2024-12-10 R. Altmann , P. Schulze

Symmetry-preserving (mimetic) discretization aims to preserve certain properties of a continuous differential operator in its discrete counterpart. For these discretizations, stability and (discrete) conservation of mass, momentum and…

Numerical Analysis · Mathematics 2019-05-13 Bas van 't Hof , Mathea J. Vuik

Physical phenomena in the real world are often described by energy-based modeling theories, such as Hamiltonian mechanics or the Landau theory, which yield various physical laws. Recent developments in neural networks have enabled the…

Numerical Analysis · Mathematics 2020-11-03 Takashi Matsubara , Ai Ishikawa , Takaharu Yaguchi

The modeling of coupled fluid transport and deformation in a porous medium is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on. Current applications of interest, for instance,…

Analysis of PDEs · Mathematics 2022-01-03 Mina Karimi , Mehrdad Massoudi , Noel Walkington , Matteo Pozzi , Kaushik Dayal

Energy-based models (EBMs) offer a flexible framework for probabilistic modelling across various data domains. However, training EBMs on data in discrete or mixed state spaces poses significant challenges due to the lack of robust and fast…

Machine Learning · Statistics 2024-12-03 Tobias Schröder , Zijing Ou , Yingzhen Li , Andrew B. Duncan

A finite element discretization using a method of lines approached is proposed for approximately solving the Poisson-Nernst-Planck (PNP) equations. This discretization scheme enforces positivity of the computed solutions, corresponding to…

Numerical Analysis · Mathematics 2015-03-17 Chun Liu , Maximilian Metti , Jinchao Xu

A novel strategy is proposed for the coupling of field and circuit equations when modeling power devices in the low-frequency regime. The resulting systems of differential-algebraic equations have a particular geometric structure which…

Numerical Analysis · Mathematics 2024-04-25 Herbert Egger , Idoia Cortes Garcia , Vsevolod Shashkov , Michael Wiesheu

Dissipative phenomena manifest in multiple mechanical systems. In this dissertation, different geometric frameworks for modelling non-conservative dynamics are considered. The objective is to generalize several results from conservative…

Mathematical Physics · Physics 2024-09-19 Asier López-Gordón

An energy-based modeling framework for the nonlinear dynamics of spatial Cosserat rods undergoing large displacements and rotations is proposed. The mixed formulation features independent displacement, velocity and stress variables and is…

Numerical Analysis · Mathematics 2026-05-11 Philipp L. Kinon , Simon R. Eugster , Peter Betsch

Efficient and stable solution of partial differential equations (PDEs) is central to scientific and engineering applications, yet existing numerical solvers rely heavily on matrix based discretizations, while learning based methods require…

Machine Learning · Computer Science 2026-04-30 Yi Bing , Zheng Ran , Fu Jinyang , Liu Long , Peng Xiang

The Cahn-Hilliard equation and extensions, notably the Cahn-Hilliard-Darcy and Cahn-Hilliard-Navier-Stokes systems, provide widely used frameworks for coupling interfacial thermodynamics with flow. This review surveys the thermodynamic…

Numerical Analysis · Mathematics 2026-02-10 Aaron Brunk , Marco F. P. ten Eikelder , Marvin Fritz , Dennis Höhn , Dennis Trautwein

This paper presents a generalized energy-based modeling framework extending recent formulations tailored for differential-algebraic equations. The proposed structure, inspired by the port-Hamiltonian formalism, ensures passivity, preserves…

Numerical Analysis · Mathematics 2026-01-06 Robert Altmann , Idoia Cortes Garcia , Elias Paakkunainen , Philipp Schulze , Sebastian Schöps

We present a natural framework for constructing energy-stable time discretization schemes. By leveraging the Onsager principle, we demonstrate its efficacy in formulating partial differential equation models for diverse gradient flow…

Numerical Analysis · Mathematics 2024-10-16 Huangxin Chen , Hailiang Liu , Xianmin Xu

In this paper we present a complete framework for the energy-stable simulation of stratified incompressible flow in channels, using the one-dimensional two-fluid model. Building on earlier energy-conserving work on the basic two-fluid…

Fluid Dynamics · Physics 2023-10-24 J. F. H. Buist , B. Sanderse , S. Dubinkina , C. W. Oosterlee , R. A. W. M. Henkes

Proposed is system of consistent mathematical models describing physical laws of a system of energy emitting bodies in dynamics, relativity and nuclear physics. It is shown the use of developed models for the description of systems,…

Dynamical Systems · Mathematics 2008-01-28 V. O. Groppen

In this paper, we propose a robust and efficient numerical framework for simulating multicomponent gas flow in poroelastic media, with a focus on preserving fundamental thermodynamic principles and ensuring computational reliability. The…

Numerical Analysis · Mathematics 2026-03-03 Huangxin Chen , Yuxiang Chen , Jisheng Kou , Shuyu Sun

We discuss structure-preserving numerical discretizations for repulsive and attractive Euler-Poisson equations that find applications in fluid-plasma and self-gravitation modeling. The scheme is fully discrete and structure preserving in…

Numerical Analysis · Mathematics 2023-05-10 Matthias Maier , John N. Shadid , Ignacio Tomas

In this study, we explore mixed-dimensional Thermo-Hydro-Mechanical (THM) models in fractured porous media accounting for Coulomb frictional contact at matrix fracture interfaces. The simulation of such models plays an important role in…

Numerical Analysis · Mathematics 2024-01-24 Jerome Droniou , Mohamed Laaziri , Roland Masson

Fast and accurate structural dynamics analysis is important for structural design and damage assessment. Structural dynamics analysis leveraging machine learning techniques has become a popular research focus in recent years. Although the…

Geophysics · Physics 2020-12-29 Yuan Feng , Hexiang Wang , Han Yang , Fangbo Wang
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