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