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 …

Learning interaction kernels in heterogeneous systems of agents from multiple trajectories

F Lu, M Maggioni, S Tang - Journal of Machine Learning Research, 2021 - jmlr.org
Systems of interacting particles, or agents, have wide applications in many disciplines,
including Physics, Chemistry, Biology and Economics. These systems are governed by …

Maximum likelihood estimation of potential energy in interacting particle systems from single-trajectory data

X Chen - Electronic Communications in Probability, 2021 - projecteuclid.org
This paper concerns the parameter estimation problem for the quadratic potential energy in
interacting particle systems from continuous-time and single-trajectory data. Even though …

On the identifiability of interaction functions in systems of interacting particles

Z Li, F Lu, M Maggioni, S Tang, C Zhang - Stochastic Processes and their …, 2021 - Elsevier
We address a fundamental issue in the nonparametric inference for systems of interacting
particles: the identifiability of the interaction functions. We prove that the interaction functions …

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 …

Mean-field analysis of multipopulation dynamics with label switching

M Morandotti, F Solombrino - SIAM Journal on Mathematical Analysis, 2020 - SIAM
The mean-field analysis of a multipopulation agent-based model is performed. The model
couples a particle dynamics driven by a nonlocal velocity with a Markov-type jump process …

Numerical identification of nonlocal potential in aggregation

Y He, SH Kang, W Liao, H Liu, Y Liu - arXiv preprint arXiv:2207.03358, 2022 - arxiv.org
Aggregation equations are broadly used to model population dynamics with nonlocal
interactions, characterized by a potential in the equation. This paper considers the inverse …

Leader formation with mean-field birth and death models

G Albi, M Bongini, F Rossi… - Mathematical Models and …, 2019 - World Scientific
We provide a mean-field description for a leader–follower dynamics with mass transfer
among the two populations. This model allows the transition from followers to leaders and …

Optimal minimax rate of learning interaction kernels

X Wang, I Seroussi, F Lu - arXiv preprint arXiv:2311.16852, 2023 - arxiv.org
Nonparametric estimation of nonlocal interaction kernels is crucial in various applications
involving interacting particle systems. The inference challenge, situated at the nexus of …