Related papers: Stochastic Variational Integrators
The purpose of this paper is to examine the Lagrangian stochastic modeling of the fluid velocity seen by inertial particles in a nonhomogeneous turbulent flow. A new Langevin-type model, compatible with the transport equation of the drift…
Reduced magnetohydrodynamics is a simplified set of magnetohydrodynamics equations with applications to both fusion and astrophysical plasmas, possessing a noncanonical Hamiltonian structure and consequently a number of conserved…
In this paper, we study the Lagrangian functions for a class of second-order differential systems arising from physics. For such systems, we present necessary and sufficient conditions for the existence of Lagrangian functions. Based on the…
The stochastic variational inference (SVI) paradigm, which combines variational inference, natural gradients, and stochastic updates, was recently proposed for large-scale data analysis in conjugate Bayesian models and demonstrated to be…
A variational framework for accelerated optimization was recently introduced on normed vector spaces and Riemannian manifolds in Wibisono et al. (2016) and Duruisseaux and Leok (2021). It was observed that a careful combination of…
We are concerned with optimization in a broad sense through the lens of solving variational inequalities (VIs) -- a class of problems that are so general that they cover as particular cases minimization of functions, saddle-point (minimax)…
Euler-Lagrange equations and variational integrators are developed for Lagrangian mechanical systems evolving on a product of two-spheres. The geometric structure of a product of two-spheres is carefully considered in order to obtain global…
In recent years, two important techniques for geometric numerical discretization have been developed. In computational electromagnetics, spatial discretization has been improved by the use of mixed finite elements and discrete differential…
In this paper, we develop the theoretical foundations of discrete Dirac mechanics, that is, discrete mechanics of degenerate Lagrangian/Hamiltonian systems with constraints. We first construct discrete analogues of Tulczyjew's triple and…
In this paper, we consider a generalization of variational calculus which allows us to consider in the same framework different cases of mechanical systems, for instance, Lagrangian mechanics, Hamiltonian mechanics, systems subjected to…
In this paper, we propose stochastic structure-preserving schemes to compute the effective diffusivity for particles moving in random flows. We first introduce the motion of particles using the Lagrangian formulation, which is modeled by…
We present a discrete analog of the recently introduced Hamilton-Pontryagin variational principle in Lagrangian mechanics. This unifies two, previously disparate approaches to discrete Lagrangian mechanics: either using the discrete…
Variational inference has experienced a recent surge in popularity owing to stochastic approaches, which have yielded practical tools for a wide range of model classes. A key benefit is that stochastic variational inference obviates the…
This paper surveys results found by the authors in the previous papers (see for example, A. Duyunova, V. Lychagin, S. Tychkov, Differential invariants for spherical layer flows of a viscid fluid, Journal of Geometry and Physics, 130,…
The recent interest in structure preserving stochastic Lagrangian and Hamiltonian systems raises questions regarding how such models are to be understood and the principles through which they are to be derived. By considering a…
The decomposition of the energy of a compressible fluid parcel into slow (deterministic) and fast (stochastic) components is interpreted as a stochastic Hamiltonian interacting particle system (HIPS). It is shown that the McKean-Vlasov…
First-order accurate degenerate variational integration (DVI) was introduced in C. L. Ellison et. al, Phys. Plasmas 25, 052502 (2018) for systems with a degenerate Lagrangian, i.e. one in which the velocity-space Hessian is singular. In…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
In this paper, we continue the construction of variational integrators adapted to contact geometry started in \cite{VBS}, in particular, we introduce a discrete Herglotz Principle and the corresponding discrete Herglotz Equations for a…
Discretizing variational principles, as opposed to discretizing differential equations, leads to discrete-time analogues of mechanics, and, systematically, to geometric numerical integrators. The phase space of such variational…