Related papers: Inference of interacting kernel in the mean-field …

For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…

We study a leader-follower system of interacting particles subject to feedback control and derive its mean-field limits through a two-step passage: first to a micro-macro system coupling leader particles with a follower fluid, and then to a…

This paper addresses the problem of learning the impulse responses characterizing forward models by means of a regularized kernel-based Prediction Error Method (PEM). The common approach to accomplish that is to approximate the system with…

In this paper we are concerned with the learnability of nonlocal interaction kernels for first order systems modeling certain social interactions, from observations of realizations of their dynamics. This paper is the first of a series on…

We propose a PDE-based accelerated gradient algorithm for optimal feedback controls of McKean-Vlasov dynamics that involve mean-field interactions both in the state and action. The method exploits a forward-backward splitting approach and…

Residual deep neural networks are formulated as interacting particle systems leading to a description through neural differential equations, and, in the case of large input data, through mean-field neural networks. The mean-field…

We investigate the interacting, one-dimensional Rice-Mele model, a prototypical fermionic model of topological properties. To set the stage, we firstly compute the single-particle spectral function, the local density, and the boundary…

This paper is concerned with the inverse problem of reconstructing a small object from far field measurements by using the field interaction with a plasmonic particle which can be viewed as a passive sensor. It is a follow-up of the work…

In this paper we establish the local and global well-posedness of weak and strong solutions to second order fractional mean-field SDEs with singular/distribution interaction kernels and measure initial value, where the kernel can be Newton…

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 vice versa, with scalar-valued transition rates depending…

This paper deals with the derivation of the mean-field limit for multi-agent systems on a large class of sparse graphs. More specifically, the case of non-exchangeable multi-agent systems consisting of non-identical agents is addressed. The…

A method is introduced to renormalize the zero-range interaction for use in mean-field and many-body theory, starting from two-body calculations. The density-renormalized delta-function interaction is then applied using mean-field theory to…

The random batch method (RBM) proposed in [Jin et al., J. Comput. Phys., 400(2020), 108877] for large interacting particle systems is an efficient with linear complexity in particle numbers and highly scalable algorithm for $N$-particle…

We consider a particle system with uniform coupling between a macroscopic component and individual particles. The constraint for each particle is of full rank, which implies that each movement of the macroscopic component leads to a…

We study an interacting particle system whose dynamics depends on an interacting random environment. As the number of particles grows large, the transition rate of the particles slows down (perhaps because they share a common resource of…

A partial differential equation (PDE) was developed to describe time-dependent ligand-receptor interactions for applications in biosensing using field effect transistors (FET). The model describes biochemical interactions at the sensor…

State-dependent networked dynamical systems are ones where the interconnections between agents change as a function of the states of the agents. Such systems are highly nonlinear, and a cohesive strategy for their control is lacking in the…

We consider the problem of controlling the group behavior of a large number of dynamic systems that are constantly interacting with each other. These systems are assumed to have identical dynamics (e.g., birds flock, robot swarm) and their…

We consider off-policy evaluation (OPE) of deterministic target policies for reinforcement learning (RL) in environments with continuous action spaces. While it is common to use importance sampling for OPE, it suffers from high variance…

We consider a system of $N\gg 1$ interacting fermionic particles in three dimensions, confined in a periodic box of volume $1$, in the mean-field scaling. We assume that the interaction potential is bounded and small enough. We prove upper…