As a counterpoint to classical stochastic particle methods for diffusion, we develop a
deterministic particle method for linear and nonlinear diffusion. At first glance, deterministic …

Given a large ensemble of interacting particles, driven by nonlocal interactions and localized
repulsion, the mean-field limit leads to a class of nonlocal, nonlinear partial differential …

Combining the classical theory of optimal transport with modern operator splitting
techniques, we develop a new numerical method for nonlinear, nonlocal partial differential …

We investigate the implementation of a new stochastic Kuramoto-Vicsek-type model for
global optimization of nonconvex functions on the sphere. This model belongs to the class of …

We introduce a new stochastic differential model for global optimization of nonconvex
functions on compact hypersurfaces. The model is inspired by the stochastic Kuramoto …

Various machine learning tasks, from generative modeling to domain adaptation, revolve
around the concept of dataset transformation and manipulation. While various methods exist …

We rigorously justify the mean-field limit of an N-particle system subject to Brownian motions
and interacting through the Newtonian potential in R^ 3 R 3. Our result leads to a derivation …

In this paper we rigorously justify the propagation of chaos for the parabolic–elliptic Keller–
Segel equation over bounded convex domains. The boundary condition under …

In this paper, we propose and study a stochastic aggregation–diffusion equation of the
Keller–Segel (KS) type for modeling the chemotaxis in dimensions d= 2, 3 d= 2, 3. Unlike the …

In this paper, we study the parameter estimation of interacting particle systems subject to the
Newtonian aggregation and Brownian diffusion. Specifically, we construct an estimator ν< …