Propagation of chaos: a review of models, methods and applications. II. Applications

LP Chaintron, A Diez - arxiv preprint arxiv:2106.14812, 2021 - arxiv.org
The notion of propagation of chaos for large systems of interacting particles originates in
statistical physics and has recently become a central notion in many areas of applied …

Consensus-based optimization on the sphere: Convergence to global minimizers and machine learning

M Fornasier, L Pareschi, H Huang, P Sünnen - Journal of Machine …, 2021 - jmlr.org
We investigate the implementation of a new stochastic Kuramoto-Vicsek-type model for
global optimization of nonconvex functions on the sphere. This model belongs to the class of …

[HTML][HTML] Learning mean-field equations from particle data using WSINDy

DA Messenger, DM Bortz - Physica D: Nonlinear Phenomena, 2022 - Elsevier
We develop a weak-form sparse identification method for interacting particle systems (IPS)
with the primary goals of reducing computational complexity for large particle number N and …

Consensus-based optimization on hypersurfaces: Well-posedness and mean-field limit

M Fornasier, H Huang, L Pareschi… - Mathematical Models and …, 2020 - World Scientific
We introduce a new stochastic differential model for global optimization of nonconvex
functions on compact hypersurfaces. The model is inspired by the stochastic Kuramoto …

On the mean‐field limit for the consensus‐based optimization

H Huang, J Qiu - Mathematical Methods in the Applied …, 2022 - Wiley Online Library
This paper is concerned with the large particle limit for the consensus‐based optimization
(CBO), which was postulated in the pioneering works by Carrillo, Pinnau, Totzeck and many …

Anisotropic diffusion in consensus-based optimization on the sphere

M Fornasier, H Huang, L Pareschi, P Sünnen - SIAM Journal on …, 2022 - SIAM
In this paper, we are concerned with the global minimization of a possibly nonsmooth and
nonconvex objective function constrained on the unit hypersphere by means of a multi-agent …

Well‐posedness of diffusion–aggregation equations with bounded kernels and their mean‐field approximations

L Chen, P Nikolaev, DJ Prömel - Mathematical Methods in the …, 2024 - Wiley Online Library
The well‐posedness and regularity properties of diffusion–aggregation equations, emerging
from interacting particle systems, are established on the whole space for bounded …

On the mean-field limit for the Vlasov–Poisson–Fokker–Planck system

H Huang, JG Liu, P Pickl - Journal of Statistical Physics, 2020 - Springer
We rigorously justify the mean-field limit of an N-particle system subject to Brownian motions
and interacting through the Newtonian potential in R^ 3 R 3. Our result leads to a derivation …

Quantitative relative entropy estimates on the whole space for convolution interaction forces

P Nikolaev, DJ Prömel - arxiv preprint arxiv:2401.08938, 2024 - arxiv.org
Quantitative estimates are derived, on the whole space, for the relative entropy between the
joint law of random interacting particles and the tensorized law at the limiting systeme. The …

The microscopic derivation and well-posedness of the stochastic Keller–Segel equation

H Huang, J Qiu - Journal of nonlinear science, 2021 - Springer
In this paper, we propose and study a stochastic aggregation–diffusion equation of the
Keller–Segel (KS) type for modeling the chemotaxis in dimensions d= 2, 3 d= 2, 3. Unlike the …