Related papers: Computational Mean-field information dynamics asso…
Recent years have seen a great increase in the capacity and parallel processing power of data centers and cloud services. To fully utilize the said distributed systems, optimal load balancing for parallel queuing architectures must be…
Nowadays, neural networks are widely used in many applications as artificial intelligence models for learning tasks. Since typically neural networks process a very large amount of data, it is convenient to formulate them within the…
We consider reaction-diffusion systems where components diffuse inside the domain and react on the surface through mass transport type boundary conditions on an evolving domain. Using Lyapunov functional and duality arguments, we establish…
We consider particle-based stochastic reaction-drift-diffusion models where particles move via diffusion and drift induced by one- and two-body potential interactions. The dynamics of the particles are formulated as measure-valued…
We investigate an optimization problem that arises when working within the paradigm of Data-Driven Computational Mechanics. In the context of the diffusion-reaction problem, such an optimization problem seeks for the continuous primal…
In the current work we consider the numerical solutions of equations of stationary states for a general class of the spatial segregation of reaction-diffusion systems with $m\geq 2$ population densities. We introduce a discrete multi-phase…
Neural network dynamics emerge from the interaction of spiking cells. One way to formulate the problem is through a theoretical framework inspired by ideas coming from statistical physics, the so-called mean-field theory. In this document,…
The problem of mass diffusion in layered systems has relevance to applications in different scientific disciplines, e.g., chemistry, material science, soil science, and biomedical engineering. The mathematical challenge in these type of…
This paper analyzes distributed control protocols for first- and second-order networked dynamical systems. We propose a class of nonlinear consensus controllers where the input of each agent can be written as a product of a nonlinear gain,…
Finding representative reaction pathways is necessary for understanding mechanisms of molecular processes, but is considered to be extremely challenging. We propose a new method to construct reaction paths based on mean first-passage times.…
A Linear-quadratic optimal control problem is considered for mean-field stochastic differential equations with deterministic coefficients. By a variational method, the optimality system is derived, which turns out to be a linear mean-field…
Phase transitions of reaction-diffusion systems with site occupation restriction and with particle creation that requires n>1 parents and where explicit diffusion of single particles (A) exists are reviewed. Arguments based on mean-field…
Brownian motion in a granular gas in a homogeneous cooling state is studied theoretically and by means of molecular dynamics. We use the simplest first-principle model for the impact-velocity dependent restitution coefficient, as it follows…
Mean-field Ring Polymer Molecular Dynamics (MF-RPMD) offers a computationally efficient method for the simulation of reaction rates in multi-level systems. Previous work has established that, to model a nonadiabatic state-to-state reaction…
The calculation of optimal structures in reaction-diffusion models is of great importance in many physicochemical systems. We propose here a simple method to monitor the number of interphases for long times by using a boundary flux…
We consider an optimal control problem where the average welfare of weakly interacting agents is of interest. We examine the mean-field control problem as the fluid approximation of the N-agent control problem with the setup of finite-state…
Direct numerical simulations and mean-field theory are used to model reactive front propagation in a turbulent medium. In the mean-field approach, memory effects of turbulent diffusion are taken into account to estimate the front speed in…
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…
We introduce the concept of {\it mean-field optimal control} which is the rigorous limit process connecting finite dimensional optimal control problems with ODE constraints modeling multi-agent interactions to an infinite dimensional…
The problem of controlling hybrid dynamical systems using model predictive control (MPC) is formulated and sufficient conditions for asymptotic stability of a set are provided. Hybrid dynamical systems are modeled in terms of hybrid…