arXiv subjects

Wenyu Dong

Publications and source records attributed to Wenyu Dong.

3 recordsLinked to original sources

arXiv2026

BTF-PINN: Enforcing Dirichlet Boundary Conditions Without Boundary Training

The homogeneous Dirichlet boundary value problem captures the core difficulty of solving Dirichlet problems with non-interpolatory methods. We propose BTF-PINN (Boundary-Training-Free Physics-Informed Neural Network), an interior-only strategy for solving homogeneous Dirichlet boundary value problems that requires no boundary training, boundary penalties, or boundary-conforming parametrizations. The key idea is to embed the essential boundary condition into a newly designed boundary-free loss function. We prove the equivalence between the proposed interior-only variational formulation and the original boundary value problem, establish a sharp threshold condition for the residual weight, and develop a convergence analysis based on the coercivity of the functional. Numerical experiments on high-dimensional problems, irregular geometries, and anisotropic elliptic equations demonstrate the effectiveness of BTF-PINN. Comparisons with standard boundary-penalty PINNs further show that BTF-PINN achieves superior boundary trace accuracy.

math.NA↗

arXiv2026

Primal finite element scheme of the Hodge-Laplace problem

In this paper, we construct nonconforming finite element spaces $\boldsymbol{V}^{\mathbf{d}\cap\mathring{\boldsymbol{\delta}}}_h\Lambda^k$ for the approximation of $H\Lambda^k\cap H^*_0\Lambda^k$ on simplicial meshes, for $n\ge 2$ and $1\le k\le n-1$, by enforcing adjoint continuity against piecewise Whitney spaces rather than trace matching. It holds, with $\mathbf{d}^k_h$ and $\boldsymbol{\delta}_{k,h}$ denoting respectively the piecewise action of differential and codifferential operators, and $\boldsymbol{\mathfrak{H}}_h\Lambda^k$ being the discrete harmonic forms in the FEEC sense, that $\boldsymbol{\mathfrak{H}}_h\Lambda^k=\{\boldsymbol{\mu}_h\in \boldsymbol{V}^{\mathbf{d}\cap\mathring{\boldsymbol{\delta}}}_h\Lambda^k:\mathbf{d}^k_h\boldsymbol{\mu}_h=0,\ \boldsymbol{\delta}_{k,h}\boldsymbol{\mu}_h=0\}$, which mirrors the continuous Hodge--Laplace kernel on domains with nontrivial topology. The space is not a classical Ciarlet-type finite element space; though, a uniform discrete Poincare inequality and locally supported basis functions (supported on at most two cells) are guaranteed. The resulting primal scheme yields an $O(h)$ error bound for smooth data and $O(h^s)$ on $s$-regular domains ($0<s\le 1$), nontrivial topology admitted. Two- and three-dimensional eigenvalue tests agree with the mixed method on perforated domains, which are given to verify the validity of the scheme.

math.NA↗

arXiv2022

Behavioral graph fraud detection in E-commerce

In e-commerce industry, graph neural network methods are the new trends for transaction risk modeling.The power of graph algorithms lie in the capability to catch transaction linking network information, which is very hard to be captured by other algorithms.However, in most existing approaches, transaction or user connections are defined by hard link strategies on shared properties, such as same credit card, same device, same ip address, same shipping address, etc. Those types of strategies will result in sparse linkages by entities with strong identification characteristics (ie. device) and over-linkages by entities that could be widely shared (ie. ip address), making it more difficult to learn useful information from graph. To address aforementioned problems, we present a novel behavioral biometric based method to establish transaction linkings based on user behavioral similarities, then train an unsupervised GNN to extract embedding features for downstream fraud prediction tasks. To our knowledge, this is the first time similarity based soft link has been used in graph embedding applications. To speed up similarity calculation, we apply an in-house GPU based HDBSCAN clustering method to remove highly concentrated and isolated nodes before graph construction. Our experiments show that embedding features learned from similarity based behavioral graph have achieved significant performance increase to the baseline fraud detection model in various business scenarios. In new guest buyer transaction scenario, this segment is a challenge for traditional method, we can make precision increase from 0.82 to 0.86 at the same recall of 0.27, which means we can decrease false positive rate using this method.

cs.LG↗