Yin Tao

Oscar P. Bruno, Liwei Xu, Tao Yin

We present a novel approach for the numerical solution of problems of elastic scattering by open arcs in two dimensions. Our methodology relies on the composition of weighted versions of the classical operators associated with Dirichlet and Neumann boundary conditions in conjunction with a certain "open-arc elastic Calderón relation" whose validity is demonstrated in this paper on the basis of numerical experiments, but whose rigorous mathematical proof is left for future work. Using this Calderón relation in conjunction with spectrally accurate quadrature rules and the Krylov-subspace linear algebra solver GMRES, the proposed overall open-arc elastic solver produces results of high accuracy in small number of iterations---for low and high frequencies alike. A variety of numerical examples in this paper demonstrate the accuracy and efficiency of the proposed methodology.

Tao Yin, Chen Zhao, Xiaoyan Liu et al.

Graph neural networks (GNNs) are proven effective in extracting complex node and structural information from graph data. While current GNNs perform well in node classification tasks within in-distribution (ID) settings, real-world scenarios often present distribution shifts, leading to the presence of out-of-distribution (OOD) nodes. OOD detection in graphs is a crucial and challenging task. Most existing research focuses on homogeneous graphs, but real-world graphs are often heterogeneous, consisting of diverse node and edge types. This heterogeneity adds complexity and enriches the informational content. To the best of our knowledge, OOD detection in heterogeneous graphs remains an underexplored area. In this context, we propose a novel methodology for OOD detection in heterogeneous graphs (OODHG) that aims to achieve two main objectives: 1) detecting OOD nodes and 2) classifying all ID nodes based on the first task's results. Specifically, we learn representations for each node in the heterogeneous graph, calculate energy values to determine whether nodes are OOD, and then classify ID nodes. To leverage the structural information of heterogeneous graphs, we introduce a meta-path-based energy propagation mechanism and an energy constraint to enhance the distinction between ID and OOD nodes. Extensive experimental findings substantiate the simplicity and effectiveness of OODHG, demonstrating its superiority over baseline models in OOD detection tasks and its accuracy in ID node classification.