A blob method for diffusion
JA Carrillo, K Craig, FS Patacchini - Calculus of Variations and Partial …, 2019 - Springer
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 …
deterministic particle method for linear and nonlinear diffusion. At first glance, deterministic …
Aggregation-diffusion equations: dynamics, asymptotics, and singular limits
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 …
repulsion, the mean-field limit leads to a class of nonlocal, nonlinear partial differential …
Primal dual methods for Wasserstein gradient flows
Combining the classical theory of optimal transport with modern operator splitting
techniques, we develop a new numerical method for nonlinear, nonlocal partial differential …
techniques, we develop a new numerical method for nonlinear, nonlocal partial differential …
Consensus-based optimization on the sphere: Convergence to global minimizers and machine learning
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 …
global optimization of nonconvex functions on the sphere. This model belongs to the class of …
Consensus-based optimization on hypersurfaces: Well-posedness and mean-field limit
We introduce a new stochastic differential model for global optimization of nonconvex
functions on compact hypersurfaces. The model is inspired by the stochastic Kuramoto …
functions on compact hypersurfaces. The model is inspired by the stochastic Kuramoto …
Dataset dynamics via gradient flows in probability space
D Alvarez-Melis, N Fusi - International conference on …, 2021 - proceedings.mlr.press
Various machine learning tasks, from generative modeling to domain adaptation, revolve
around the concept of dataset transformation and manipulation. While various methods exist …
around the concept of dataset transformation and manipulation. While various methods exist …
On the mean-field limit for the Vlasov–Poisson–Fokker–Planck system
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 …
and interacting through the Newtonian potential in R^ 3 R 3. Our result leads to a derivation …
[HTML][HTML] Propagation of chaos for the Keller–Segel equation over bounded domains
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 …
Segel equation over bounded convex domains. The boundary condition under …
The microscopic derivation and well-posedness of the stochastic Keller–Segel equation
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 …
Keller–Segel (KS) type for modeling the chemotaxis in dimensions d= 2, 3 d= 2, 3. Unlike the …
Learning interacting particle systems: Diffusion parameter estimation for aggregation equations
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< …
Newtonian aggregation and Brownian diffusion. Specifically, we construct an estimator ν< …