3 citations · 4 across the 7 of their papers we have counts for
8 papers
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 Nonlocal -Laplacian Interface Model with Sharp Interface
Kehan Shi, Zuoqiang Shi, Tangjun Wang
We propose an energy-based nonlocal -Laplacian interface problem. Neumann interface conditions are naturally formulated via the energy, while Dirichlet conditions are enforced t…
A Nonlocal Biharmonic Model with -Convergence to Local Model and an Efficient Numerical Method
Weiye Gan, Tangjun Wang, Qiang Du +1
Nonlocal models and their associated theories have been extensively investigated in recent years. Among these, nonlocal versions of the classical Laplace operator have attracted th…
Interface Laplace Learning: Learnable Interface Term Helps Semi-Supervised Learning
Tangjun Wang, Chenglong Bao, Zuoqiang Shi
We introduce a novel framework, called Interface Laplace learning, for graph-based semi-supervised learning. Motivated by the observation that an interface should exist between dif…
Convection-Diffusion Equation: A Theoretically Certified Framework for Neural Networks
Tangjun Wang, Chenglong Bao, Zuoqiang Shi
In this paper, we study the partial differential equation models of neural networks. Neural network can be viewed as a map from a simple base model to a complicate function. Based…
An axiomatized PDE model of deep neural networks
Tangjun Wang, Wenqi Tao, Chenglong Bao +1
Inspired by the relation between deep neural network (DNN) and partial differential equations (PDEs), we study the general form of the PDE models of deep neural networks. To achiev…
A Nonlocal diffusion model with convergence for Dirichlet Boundary
Tangjun Wang, Zuoqiang Shi
In this paper, we present a nonlocal model for Poisson equation and corresponding eigenproblem with Dirichlet boundary condition. In the direct derivation of the nonlocal model, no…
Diffusion Mechanism in Residual Neural Network: Theory and Applications
Tangjun Wang, Zehao Dou, Chenglong Bao +1
Diffusion, a fundamental internal mechanism emerging in many physical processes, describes the interaction among different objects. In many learning tasks with limited training sam…