37 citations · 43 across the 6 of their papers we have counts for
6 papers
Some properties on the reversibility and the linear response theory of Langevin dynamics
Yuan Gao, Jian-Guo Liu, Zibu Liu
Linear response theory is a fundamental framework studying the macroscopic response of a physical system to an external perturbation. This paper focuses on the rigorous mathematica…
Diffusion approximations of Oja's online principal component analysis
Jian-Guo Liu, Zibu Liu
Oja's algorithm of principal component analysis (PCA) has been one of the methods utilized in practice to reduce dimension. In this paper, we focus on the convergence property of t…
Convergence of Oja's online principal component flow
Jian-Guo Liu, Zibu Liu
Online principal component analysis (PCA) has been an efficient tool in practice to reduce dimension. However, convergence properties of the corresponding ODE are still unknown, in…
Existence and rigidity of the Peierls-Nabarro model for dislocations in high dimensions
Yuan Gao, Jian-Guo Liu, Zibu Liu
We focus on existence and rigidity problems of the vectorial Peierls-Nabarro (PN) model for dislocations. Under the assumption that the misfit potential on the slip plane only depe…
A stochastic version of Stein Variational Gradient Descent for efficient sampling
Lei Li, Yingzhou Li, Jian-Guo Liu +2
We propose in this work RBM-SVGD, a stochastic version of Stein Variational Gradient Descent (SVGD) method for efficiently sampling from a given probability measure and thus useful…
On Runge-Kutta methods for the water wave equation and its simplified nonlocal hyperbolic model
Lei Li, Jian-Guo Liu, Zibu Liu +2
There is a growing interest in investigating numerical approximations of the water wave equation in recent years, whereas the lack of rigorous analysis of its time discretization i…