209 citations · 1.4k across the 114 of their papers we have counts for
14 papers · 1 filter
Random batch methods (RBM) for interacting particle systems
Shi Jin, Lei Li, Jian-Guo Liu
We develop Random Batch Methods for interacting particle systems with large number of particles. These methods use small but random batches for particle interactions, thus the comp…
Large time behavior, bi-Hamiltonian structure and kinetic formulation for complex Burgers equation
Yu Gao, Yuan Gao, Jian-Guo Liu
We prove the existence and uniqueness of positive analytical solutions with positive initial data to the mean field equation (the Dyson equation) of the Dyson Brownian motion throu…
On mean field limit for Brownian particles with Coulomb interaction in 3D
Lei Li, Jian-Guo Liu, Pu Yu
In this paper, we consider the mean field limit of Brownian particles with Coulomb interaction in 3D space. In particular, using a symmetrization technique, we show that the limit…
Long-time dynamics for a simple aggregation equation on the sphere
Amic Frouvelle, Jian-Guo Liu
We give a complete study of the asymptotic behavior of a simple model of alignment of unit vectors, both at the level of particles , which corresponds to a system of coupled differ…
Well-posedness and derivative blow-up for a dispersionless regularized shallow water system
Jian-Guo Liu, Robert L. Pego, Yue Pu
We study local-time well-posedness and breakdown for solutions of regularized Saint-Venant equations (regularized classical shallow water equations) recently introduced by Clamond…
Plane-wave analysis of a hyperbolic system of equations with relaxation in
Maarten V. de Hoop, Jian-Guo Liu, Peter A. Markowich +1
We consider a multi-dimensional scalar wave equation with memory corresponding to the viscoelastic material described by a generalized Zener model. We deduce that this relaxation s…
On the rate of convergence of empirical measure in Wasserstein distance for unbounded density function
Anning Liu, Jian-Guo Liu, Yulong Lu
We consider a sequence of identically independently distributed random samples from an absolutely continuous probability measure in one dimension with unbounded density. We establi…
Large time behaviors of upwind schemes by jump processes
Lei Li, Jian-Guo Liu
We revisit the traditional upwind schemes for linear conservation laws in the viewpoint of jump processes, allowing studying upwind schemes using probabilistic tools. In particular…
Data clustering based on Langevin annealing with a self-consistent potential
Kyle Lafata, Zhennan Zhou, Jian-Guo Liu +1
This paper introduces a novel data clustering algorithm based on Langevin dynamics, where the associated potential is constructed directly from the data. To introduce a self-consis…
Global stability for solutions to the exponential PDE describing epitaxial growth
Jian-Guo Liu, Robert M. Strain
In this paper we prove the global existence, uniqueness, optimal large time decay rates, and uniform gain of analyticity for the exponential PDE in the whole space $…
On the mean-field limit for the Vlasov-Poisson-Fokker-Planck system
Hui Huang, Jian-Guo Liu, Peter Pickl
We rigorously justify the mean-field limit of a -particle system subject to the Brownian motion and interacting through a Newtonian potential in . Our result leads…
Analysis and computation of some tumor growth models with nutrient: from cell density models to free boundary dynamics
Jian-Guo Liu, Min Tang, Li Wang +1
In this paper, we study the tumor growth equation along with various models for the nutrient component, including the \emph{in vitro} model and the \emph{in vivo} model. At the cel…
Learning interacting particle systems: diffusion parameter estimation for aggregation equations
Hui Huang, Jian-Guo Liu, Jianfeng Lu
In this article, we study the parameter estimation of interacting particle systems subject to the Newtonian aggregation and Brownian diffusion. Specifically, we construct an estima…
Semi-groups of stochastic gradient descent and online principal component analysis: properties and diffusion approximations
Yuanyuan Feng, Lei Li, Jian-Guo Liu
We study the Markov semigroups for two important algorithms from machine learning: stochastic gradient descent (SGD) and online principal component analysis (PCA). We investigate t…