Geometric deep learning (GDL) models have demonstrated a great potential for the analysis of non-Euclidian data. They are developed to incorporate the geometric and topological information of non-Euclidian data into the end-to-end deep learning architectures. Motivated by the recent success of discrete Ricci curvature in graph neural network (GNNs), we propose TorGNN, an analytic Torsion enhanced Graph Neural Network model. The essential idea is to characterize graph local structures with an analytic torsion based weight formula. Mathematically, analytic torsion is a topological invariant that can distinguish spaces which are homotopy equivalent but not homeomorphic. In our TorGNN, for each edge, a corresponding local simplicial complex is identified, then the analytic torsion (for this local simplicial complex) is calculated, and further used as a weight (for this edge) in message-passing process. Our TorGNN model is validated on link prediction tasks from sixteen different types of networks and node classification tasks from three types of networks. It has been found that our TorGNN can achieve superior performance on both tasks, and outperform various state-of-the-art models. This demonstrates that analytic torsion is a highly efficient topological invariant in the characterization of graph structures and can significantly boost the performance of GNNs.
Get Rid of Suspended Animation Problem: Deep Diffusive Neural Network on Graph Semi-Supervised Classification
IFM Lab, Florida State University（佛罗里达州立大学IFM实验室）；Florida State University（佛罗里达州立大学）；IFM Lab（IFM实验室）；Tallahassee（塔拉哈西（此处按要求不应提取，但原文本中Tallahassee为城市名，根据规则应忽略，仅保留明确机构部分））
Engineering application of physics-informed neural networks for Saint-Venant torsion
Department of Quantum System Engineering, Jeonbuk National University（全量子系统工程系，全州国立大学）；Department of Mathematics, Inha University（数学系，inha大学）；Electrified Propulsion Structure CAE Team, Hyundai Motor Company（电动推进结构CAE团队，现代汽车公司）；Department of Mechanical Engineering, Inha University（机械工程系，inha大学）；Graduate School of Integrated Energy-AI, Jeonbuk National University（整合能源-人工智能研究生院，全州国立大学）
