69 citations · 518 across the 94 of their papers we have counts for
24 papers · 1 filter
Weighted Laplacian Flow: A Deterministic Particle Flow with Exponential Convergence
Weiye Gan, Tangjun Wang, Zuoqiang Shi
We introduce weighted Laplacian flow (WLF), a deterministic particle-flow framework for sampling from a target distribution known only up to normalization. The proposed method evol…
A High-Order Surface Finite Element Method Based on Intersections with Background Tetrahedral Meshes
Zibo Zhao, Zuoqiang Shi
This paper develops a high-order surface finite element method for elliptic equations posed on a smooth closed surface implicitly defined as the zero level set of a function in thr…
ND-TNN: Tensor-Neural-Network Approximation for High-Dimensional Nonlocal Diffusion Models
Ziyue Cai, Zuoqiang Shi
We study a numerical method, built on the tensor neural network (TNN) architecture introduced in \cite{wang2022tensor}, for solving nonlocal diffusion models in high-dimensional sp…
When surface evolution meets Fokker-Planck equation: a novel tangential velocity model for uniform parametrization
Jiangong Pan, Guozhi Dong, Hailong Guo +1
A common issue in simulating geometric evolution of surfaces is unexpected clustering of points that may cause numerical instability. We propose a novel artificial tangential veloc…
High-Order Quadrature for Implicitly Defined Surfaces and Regions
Zibo Zhao, Zuoqiang Shi
We propose a high-order quadrature method for integrating over curves, surfaces, and enclosed regions defined implicitly as zero level sets of smooth functions. The method combines…
On the implementation of linear finite element method for nonlocal diffusion model over 2D domain
Zuoqiang Shi
We propose an implementation of linear finite element method for nonlocal diffusion problem in 2D space. In the implementation, we reduce the integral from 4D to 2D which would sim…