Zobrazeno 1 - 10
of 129
pro vyhledávání: '"Schlichting, André"'
We study the limiting dynamics of a large class of noisy gradient descent systems in the overparameterized regime. In this regime the set of global minimizers of the loss is large, and when initialized in a neighbourhood of this zero-loss set a noisy
Externí odkaz:
http://arxiv.org/abs/2404.12293
Autor:
Lam, Chun Yin, Schlichting, André
We consider the thermodynamic limit of mean-field stochastic particle systems on a complete graph. The evolution of occupation number at each vertex is driven by particle exchange with its rate depending on the population of the starting vertex and t
Externí odkaz:
http://arxiv.org/abs/2401.06696
We propose a spatial discretization of the fourth-order nonlinear DLSS equation on the circle. Our choice of discretization is motivated by a novel gradient flow formulation with respect to a metric that generalizes martingale transport. The discrete
Externí odkaz:
http://arxiv.org/abs/2312.13284
In this note we continue the study of nonlocal interaction dynamics on a sequence of infinite graphs, extending the results of [Esposito et. al 2023+] to an arbitrary number of species. Our analysis relies on the observation that the graph dynamics f
Externí odkaz:
http://arxiv.org/abs/2306.17414
We study a class of nonlocal partial differential equations presenting a tensor-mobility, in space, obtained asymptotically from nonlocal dynamics on localising infinite graphs. Our strategy relies on the variational structure of both equations, bein
Externí odkaz:
http://arxiv.org/abs/2306.03475
In this paper, we explore the convergence of the semi-discrete Scharfetter-Gummel scheme for the aggregation-diffusion equation using a variational approach. Our investigation involves obtaining a novel gradient structure for the finite volume space
Externí odkaz:
http://arxiv.org/abs/2306.02226
We study a variant of the dynamical optimal transport problem in which the energy to be minimised is modulated by the covariance matrix of the distribution. Such transport metrics arise naturally in mean-field limits of certain ensemble Kalman method
Externí odkaz:
http://arxiv.org/abs/2302.07773
Autor:
Peletier, Mark A., Schlichting, André
We review a class of gradient systems with dissipation potentials of hyperbolic-cosine type. We show how such dissipation potentials emerge in large deviations of jump processes, multi-scale limits of diffusion processes, and more. We show how the ex
Externí odkaz:
http://arxiv.org/abs/2203.05435
Error estimates for a finite volume scheme for advection-diffusion equations with rough coefficients
Publikováno v:
ESAIM: M2AN, 2023
We study the implicit upwind finite volume scheme for numerically approximating the advection-diffusion equation with a vector field in the low regularity DiPerna-Lions setting. That is, we are concerned with advecting velocity fields that are spatia
Externí odkaz:
http://arxiv.org/abs/2201.10411
This paper contains two main contributions. First, it provides optimal stability estimates for advection-diffusion equations in a setting in which the velocity field is Sobolev regular in the spatial variable. This estimate is formulated with the hel
Externí odkaz:
http://arxiv.org/abs/2102.07759