Related papers: Critical Transitions in Interacting Particle Syste…
Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an…
This article proposes a unified framework to study non-exchangeable mean-field particle systems with some general interaction mechanisms. The starting point is a fixed-point formulation of particle systems originally due to Tanaka that…
A discrete time stochastic model for a multiagent system given in terms of a large collection of interacting Markov chains is studied. The evolution of the interacting particles is described through a time inhomogeneous transition…
In this study, we consider an optimal control problem driven by a stochastic differential equation with state constraints. Here, the state constraints mean the constraints about the path of state. In order to show the maximum principe for…
We reassess the concept of transition at minimum work in classical stochastic finite-time thermodynamics, when the system dynamics is modelled by a diffusion process. We show that a well-posed formulation of the optimal control problem…
We study the optimal transport problem for pairs of stationary finite-state Markov chains, with an emphasis on the computation of optimal transition couplings. Transition couplings are a constrained family of transport plans that capture…
We discuss the dynamics and thermodynamics of systems with long-range interactions. We contrast the microcanonical description of an isolated Hamiltonian system to the canonical description of a stochastically forced Brownian system. We…
A dynamical system entrains to a periodic input if its state converges globally to an attractor with the same period. In particular, for a constant input the state converges to a unique equilibrium point for any initial condition. We…
We consider a class of optimal control problems, with finite or infinite horizon, for a continuous-time Markov chain with finite state space. In this case, the control process affects the transition rates. We suppose that the controlled…
Mean-field stochastic differential equations, also called McKean--Vlasov equations, are the limiting equations of interacting particle systems with fully symmetric interaction potential. Such systems play an important role in a variety of…
Among various rare events, the effective computation of transition paths connecting metastable states in a stochastic model is an important problem. This paper proposes a stochastic optimal control formulation for transition path problems…
The effectiveness of collective navigation of biological or artificial agents requires to accommodate for contrasting requirements, such as staying in a group while avoiding close encounters and at the same time limiting the energy…
The population biology model holds a significant position within ecosystems. Introducing stochastic perturbations into the model can more accurately depict real biological processes. In this paper, we primarily investigate the most probable…
This paper rigorously connects the problem of optimal control of McKean-Vlasov dynamics with large systems of interacting controlled state processes. Precisely, the empirical distributions of near-optimal control-state pairs for the…
Chemical reactions can be modelled via diffusion processes conditioned to make a transition between specified molecular configurations representing the state of the system before and after the chemical reaction. In particular the model of…
Active systems, which are driven out of equilibrium by local non-conservative forces, exhibit unique behaviors and structures with potential utility for the design of novel materials. An important and difficult challenge along the path…
Recent work linking deep neural networks and dynamical systems opened up new avenues to analyze deep learning. In particular, it is observed that new insights can be obtained by recasting deep learning as an optimal control problem on…
Propagation of chaos for interacting particle systems has been an active research topic over decades. We propose an alternative approach to study the mean-field limit of the stochastic interacting particle systems via tools from information…
In this paper, we present a rigorous derivation of the mean-field limit for a moderately interacting particle system in $\R^d$ $(d\geq 2)$. For stochastic initial data, we demonstrate that the solution to the interacting particle model,…
We develop a variational neural-network framework to determine the most probable path (MPP) of a 3D active Brownian particle (ABP) by directly minimizing the Onsager-Machlup integral (OMI). To obtain the OMI, we use the Onsager-Machlup…