Publications
Interface Laplace Learning: Learnable Interface Term Helps Semi-Supervised Learning
Tangjun Wang, Chenglong Bao, Zuoqiang Shi
CSIAM Transactions on Applied Mathematics (to appear) · 2025
An improvement over Laplace learning that explicitly models the interface between different classes, significantly improving performance under extremely low label rates.
A Nonlocal Biharmonic Model with Γ-Convergence to Local Model and an Efficient Numerical Method
Weiye Gan, Tangjun Wang, Qiang Du, Zuoqiang Shi
Preprint · 2025
A nonlocal biharmonic model with clamped boundary condition, together with an efficient finite element method.
Convection-Diffusion Equation: A Theoretically Certified Framework for Neural Networks
Tangjun Wang, Chenglong Bao, Zuoqiang Shi
IEEE Transactions on Pattern Analysis and Machine Intelligence · 2025
An axiomatic framework that bridges neural networks and PDEs via a convection–diffusion formulation, together with a novel PDE-inspired network architecture (COIN).
A Nonlocal diffusion model with H¹ convergence for Dirichlet Boundary
Tangjun Wang, Zuoqiang Shi
Communications in Mathematical Sciences · 2024
A nonlocal diffusion model with first-order H¹ convergence that enforces Dirichlet boundary conditions by introducing the normal derivative as an auxiliary variable.
Diffusion Mechanism in Residual Neural Network: Theory and Applications
Tangjun Wang, Zehao Dou, Chenglong Bao, Zuoqiang Shi
IEEE Transactions on Pattern Analysis and Machine Intelligence · 2024
A diffusion-enhanced residual neural network (Diff-ResNet) inspired by convection–diffusion ODEs, with theoretical guarantees on improving class separability.