Zobrazeno 1 - 10
of 303
pro vyhledávání: '"Peletier, Mark"'
We study a system of stochastic differential equations with singular drift which describes the dynamics of signed particles in two dimensions interacting by the Coulomb potential. In contrast to the well-studied cases of identical particles that eith
Externí odkaz:
http://arxiv.org/abs/2410.15855
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
We reconsider the fundamental problem of coarse-graining infinite-dimensional Hamiltonian dynamics to obtain a macroscopic system which includes dissipative mechanisms. In particular, we study the thermodynamical implications concerning Hamiltonians,
Externí odkaz:
http://arxiv.org/abs/2404.09284
Neural Stochastic Differential Equations (NSDE) have been trained as both Variational Autoencoders, and as GANs. However, the resulting Stochastic Differential Equations can be hard to interpret or analyse due to the generic nature of the drift and d
Externí odkaz:
http://arxiv.org/abs/2211.09537
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
Autor:
Baumeier, Björn, Çaylak, Onur, Mercuri, Carlo, Peletier, Mark, Prokert, Georg, Scharpach, Wouter
Publikováno v:
In Journal of Mathematical Analysis and Applications 15 January 2025 541(2)
We study the asymptotic behaviour of a gradient system in a regime in which the driving energy becomes singular. For this system gradient-system convergence concepts are ineffective. We characterize the limiting behaviour in a different way, by provi
Externí odkaz:
http://arxiv.org/abs/2105.03401
Autor:
Manita, Oxana A., Peletier, Mark A., Portegies, Jacobus W., Sanders, Jaron, Senen-Cerda, Albert
We prove two universal approximation theorems for a range of dropout neural networks. These are feed-forward neural networks in which each edge is given a random $\{0,1\}$-valued filter, that have two modes of operation: in the first each edge output
Externí odkaz:
http://arxiv.org/abs/2012.10351
Autor:
Baumeier, Björn, Çaylak, Onur, Mercuri, Carlo, Peletier, Mark, Prokert, Georg, Scharpach, Wouter
We prove existence and uniqueness of solutions to the initial-value problem associated with a class of time-dependent Kohn-Sham equations coupled with Newtonian nuclear dynamics. We consider a pure power exchange term within a generalisation of the L
Externí odkaz:
http://arxiv.org/abs/2011.10542
We consider nonlinear reaction systems satisfying mass-action kinetics with slow and fast reactions. It is known that the fast-reaction-rate limit can be described by an ODE with Lagrange multipliers and a set of nonlinear constraints that ask the fa
Externí odkaz:
http://arxiv.org/abs/2010.08458