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This paper analyzes and explicitly solves a class of long-term average impulse control problems with a specific mean-field interaction. The underlying process is a general one-dimensional diffusion with appropriate boundary behavior. The…

Optimization and Control · Mathematics 2026-02-04 K. L. Helmes , R. H. Stockbridge , C. Zhu

A system of interacting Brownian particles subject to short-range repulsive potentials is considered. A continuum description in the form of a nonlinear diffusion equation is derived systematically in the dilute limit using the method of…

Statistical Mechanics · Physics 2017-10-12 Maria Bruna , S. Jonathan Chapman , Martin Robinson

Following Kolokoltsov's work [1], we present an extension of mean-field control theory in quantum framework. In particular such an extension is done naturally by considering the Belavkin quantum filtering and control theory in a mean-field…

Optimization and Control · Mathematics 2023-06-27 Sofiane Chalal , Nina H. Amini , Gaoyue Guo

A mean-field model to describe electron transfer processes in ion-molecule collisions at the $\hbar =0$ level is presented and applied to collisions involving water and ammonia molecules. Multicenter model potentials account for the…

Atomic Physics · Physics 2023-11-21 Alba Jorge , Marko Horbatsch , Tom Kirchner

Empirically derived continuum models of collective behavior among large populations of dynamic agents are a subject of intense study in several fields, including biology, engineering and finance. We formulate and study a mean-field game…

Adaptation and Self-Organizing Systems · Physics 2018-06-22 Piyush Grover , Kaivalya Bakshi , Evangelos A. Theodorou

We establish the existence of solutions to a class of non-linear stochastic differential equation of reaction-diffusion type in an infinite-dimensional space, with diffusion corresponding to a given transition kernel. The solution obtained…

Probability · Mathematics 2021-08-10 Conrado da Costa , Bernardo Freitas Paulo da Costa , Daniel Valesin

We consider a class of optimization problems on the space of probability measures motivated by the mean-field approach to studying neural networks. Such problems can be solved by constructing continuous-time gradient flows that converge to…

Optimization and Control · Mathematics 2026-02-18 Petra Lazić , Linshan Liu , Mateusz B. Majka

The main difficulty that arises in the analysis of most machine learning algorithms is to handle, analytically and numerically, a large number of interacting random variables. In this Ph.D manuscript, we revisit an approach based on the…

Disordered Systems and Neural Networks · Physics 2021-03-11 Benjamin Aubin

This paper deals with the solution of unified fractional reaction-diffusion systems. The results are obtained in compact and elegant forms in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for…

Classical Analysis and ODEs · Mathematics 2014-09-11 R. K. Saxena , A. M. Mathai , H. J. Haubold

We study reaction-diffusion equations in cylinders with possibly nonlinear diffusion and possibly nonlinear Neumann boundary conditions. We provide a geometric Poincar\'e-type inequality and classification results for stable solutions, and…

Analysis of PDEs · Mathematics 2016-06-28 Serena Dipierro , Nicola Soave , Enrico Valdinoci

The goal of this work is to compute a boundary control of reaction-diffusion partial differential equation. The boundary control is subject to a constant delay, whereas the equation may be unstable without any control. For this system…

Analysis of PDEs · Mathematics 2017-09-11 Christophe Prieur , Emmanuel Trélat

In this paper, we propose an efficient and flexible algorithm to solve dynamic mean-field planning problems based on an accelerated proximal gradient method. Besides an easy-to-implement gradient descent step in this algorithm, a crucial…

Optimization and Control · Mathematics 2021-03-01 Jiajia Yu , Rongjie Lai , Wuchen Li , Stanley Osher

This paper applies a discrete adjoint gradient computation method for a multi-class traffic flow model on road networks. Vehicle classes are characterized by their specific velocity functions, which depend on the total traffic density,…

Analysis of PDEs · Mathematics 2026-04-02 Paola Goatin , Axel Klar , Carmen Mezquita-Nieto

In this paper we study a class of matrix-valued linear-quadratic mean-field-type games for both the risk-neutral, risk-sensitive and robust cases. Non-cooperation, full cooperation and adversarial between teams are treated. We provide a…

Optimization and Control · Mathematics 2019-06-06 Julian Barreiro-Gomez , Tyrone E. Duncan , Hamidou Tembine

In this work we discuss an Mean Field Games approach to traffic management on multi-lane roads. Such approach is particularly indicated to model self driven vehicles with perfect information of the domain. The mathematical interest of the…

Optimization and Control · Mathematics 2018-05-14 Adriano Festa , Simone Göttlich

We formulate a class of mean field games on a finite state space with variational principles resembling those in continuous-state mean field games. We construct a controlled continuity equation featuring a nonlinear activation function on…

Optimization and Control · Mathematics 2023-10-10 Yuan Gao , Wuchen Li , Jian-Guo Liu

We study a class of variational problems for regularized conservation laws with Lax's entropy-entropy flux pairs. We first introduce a modified optimal transport space based on conservation laws with diffusion. Using this space, we…

Analysis of PDEs · Mathematics 2021-11-11 Wuchen Li , Siting Liu , Stanley Osher

In this paper we consider mean-field optimal control problems with selective action of the control, where the constraint is a continuity equation involving a non-local term and diffusion. First order optimality conditions are formally…

Optimization and Control · Mathematics 2023-02-02 Giacomo Albi , Marco Caliari , Elisa Calzola , Fabio Cassini

The problem of communicating sensor measurements over shared networks is prevalent in many modern large-scale distributed systems such as cyber-physical systems, wireless sensor networks, and the internet of things. Due to bandwidth…

Systems and Control · Electrical Eng. & Systems 2021-12-14 Marcos M. Vasconcelos

The problem of estimating the reaction coefficient of a system governed by a reaction-diffusion partial differential equation is tackled. An estimator relying on boundary measurements only is proposed. The estimator is based upon a setpoint…

Optimization and Control · Mathematics 2024-05-10 Gildas Besançon , Andrea Cristofaro , Francesco Ferrante