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We experimentally and theoretically study the thermodynamically optimal control of interacting multiple-particle systems, focusing on collections of colloidal particles individually confined in optical traps. We investigate protocols that…

Soft Condensed Matter · Physics 2026-03-19 Samuel Monter , Lars T. Stutzer , Sarah A. M. Loos , Clemens Bechinger

This article is concerned with stochastic control problems for backward doubly stochastic differential equations of mean-field type, where the coefficient functions depend on the joint distribution of the state process and the control…

Probability · Mathematics 2022-05-26 Jian Song , Meng Wang

We consider interacting agent systems with a large number of stochastic agents (or particles) influenced by a fixed number of external stochastic lead agents. Such examples arise, for example in models of opinion dynamics, where a small…

Optimization and Control · Mathematics 2025-12-23 Sebastian Zimper , Ana Djurdjevac , Carsten Hartmann , Christof Schütte , Nataša Djurdjevac Conrad

We study the convergence of an $N$-particle Markovian controlled system to the solution of a family of stochastic McKean-Vlasov control problems, either with a finite horizon or Schr\"odinger type cost functional. Specifically, under…

Probability · Mathematics 2024-05-22 Francesco C. De Vecchi , Chiara Rigoni

We present a data-driven point of view for rare events, which represent conformational transitions in biochemical reactions modeled by over-damped Langevin dynamics on manifolds in high dimensions. We first reinterpret the transition state…

Optimization and Control · Mathematics 2023-04-06 Yuan Gao , Tiejun Li , Xiaoguang Li , Jian-Guo Liu

Controlling large particle systems in collective dynamics by a few agents is a subject of high practical importance, e.g., in evacuation dynamics. In this paper we study an instantaneous control approach to steer an interacting particle…

Optimization and Control · Mathematics 2020-01-29 Martin Burger , Rene Pinnau , Claudia Totzeck , Oliver Tse , Andreas Roth

In this paper we consider a mean field optimal control problem with an aggregation-diffusion constraint, where agents interact through a potential, in the presence of a Gaussian noise term. Our analysis focuses on a PDE system coupling a…

Analysis of PDEs · Mathematics 2019-09-25 Jose A. Carrillo , Edgard A. Pimentel , Vardan K. Voskanyan

In this article, we study an interacting particle system in the context of epidemiology where the individuals (particles) are characterized by their position and infection state. We begin with a description at the microscopic level where…

Probability · Mathematics 2022-12-06 Maxime Hauray , Etienne Pardoux , Yen V. Vuong

Transition of a system between two states is an important but difficult problem in natural science. In this article we study the transition problem in the framework of transition path ensemble. Using the overdamped Langevin method, we…

Statistical Mechanics · Physics 2023-02-01 De-Zhang Li , Jia-Rui Zeng , Wei-Jie Huang , Yao Yao , Xiao-Bao Yang

A mean-field selective optimal control problem of multipopulation dynamics via transient leadership is considered. The agents in the system are described by their spatial position and their probability of belonging to a certain population.…

Optimization and Control · Mathematics 2021-06-15 Giacomo Albi , Stefano Almi , Marco Morandotti , Francesco Solombrino

Focusing on stochastic systems arising in mean-field models, the systems under consideration belong to the class of switching diffusions, in which continuous dynamics and discrete events coexist and interact. The discrete events are modeled…

Probability · Mathematics 2019-01-18 Son L. Nguyen , George Yin , Tuan A. Hoang

We investigate the theoretical and numerical computation of rare transitions in simple geophysical turbulent models. We consider the barotropic quasi-geostrophic and two-dimensional Navier-Stokes equations in regimes where bistability…

Statistical Mechanics · Physics 2015-03-10 Jason Laurie , Freddy Bouchet

We present a unified framework, with quantitative estimates, for deterministic interacting particle systems whose pairwise interactions may depend on heterogeneous labels. Heterogeneity is kept at every level by adding a frozen label…

Analysis of PDEs · Mathematics 2026-05-21 Thierry Paul , Emmanuel Trélat

We consider mean-field interactions corresponding to Gibbs measures on interacting Brownian paths in three dimensions. The interaction is self-attractive and is given by a singular Coulomb potential. The logarithmic asymptotics of the…

Probability · Mathematics 2017-10-25 Erwin Bolthausen , Wolfgang Koenig , Chiranjib Mukherjee

For a certain class of McKean-Vlasov processes, we introduce proxy processes that substitute the mean-field interaction with self-interaction, employing a weighted occupation measure. Our study encompasses two key achievements. First, we…

Probability · Mathematics 2025-11-04 Kai Du , Zhenjie Ren , Florin Suciu , Songbo Wang

We consider the stochastic control of a semi-linear stochastic partial differential equations (SPDE) of McKean-Vlasov type. Based on a recent novel approach to the Lions derivative for Banach space valued functions, we prove the Gateaux…

Probability · Mathematics 2025-08-12 Johan Benedikt Spille , Wilhelm Stannat

We consider the control of McKean-Vlasov dynamics whose coefficients have mean field interactions in the state and control. We show that for a class of linear-convex mean field control problems, the unique optimal open-loop control admits…

Optimization and Control · Mathematics 2021-09-27 Christoph Reisinger , Wolfgang Stockinger , Yufei Zhang

In this paper, we study weakly interacting diffusion processes on random graphs. Our main focus is on the properties of the mean-field limit and, in particular, on the nonuniqueness and bifurcation structure of stationary states. By…

Dynamical Systems · Mathematics 2025-11-03 Benedetta Bertoli , Grigorios A. Pavliotis , Niccolò Zagli

We propose a particle system of diffusion processes coupled through a chain-like network structure described by an infinite-dimensional, nonlinear stochastic differential equation of McKean-Vlasov type. It has both (i) a local chain…

Probability · Mathematics 2019-07-18 Nils Detering , Jean-Pierre Fouque , Tomoyuki Ichiba

The purpose of this paper is to study optimal control of conditional McKean-Vlasov (mean-field) stochastic differential equations with jumps (conditional McKean-Vlasov jump diffusions, for short). To this end, we first prove a stochastic…

Probability · Mathematics 2023-01-10 Nacira Agram , Bernt Oksendal