Traditional simulation of complex mechanical systems relies on numerical solvers of Partial Differential Equations (PDEs), e.g., using the Finite Element Method (FEM). The FEM solvers frequently suffer from intensive computation cost and high running time. Recent graph neural network (GNN)-based simulation models can improve running time meanwhile with acceptable accuracy. Unfortunately, they are hard to tailor GNNs for complex mechanical systems, including such disadvantages as ineffective representation and inefficient message propagation (MP). To tackle these issues, in this paper, with the proposed Up-sampling-only and Adaptive MP techniques, we develop a novel hierarchical Mesh Graph Network, namely UA-MGN, for efficient and effective mechanical simulation. Evaluation on two synthetic and one real datasets demonstrates the superiority of the UA-MGN. For example, on the Beam dataset, compared to the state-of-the-art MS-MGN, UA-MGN leads to 40.99% lower errors but using only 43.48% fewer network parameters and 4.49% fewer floating point operations (FLOPs).
Efficient Learning of Mesh-Based Physical Simulation with BSMS-GNN
Department of Computer Science, UCLA, Los Angeles, USA（加州大学洛杉矶分校计算机科学系）；AR Perception, Google, Los Angeles, USA（谷歌AR感知部门）；Department of Mathematics, UCLA, Los Angeles, USA（加州大学洛杉矶分校数学系）
MAVEN: A Mesh-Aware Volumetric Encoding Network for Simulating 3D Flexible Deformation
Academy for Advanced Interdisciplinary Studies, Peking University（北京大学前沿交叉学科研究院）；School of Computer Science, Peking University（北京大学计算机学院）；School of Electrical and Computer Science, University of Southampton（南安普顿大学电气与计算机科学学院）
Mesh-based Super-Resolution of Fluid Flows with Multiscale Graph Neural Networks
Transportation and Power Systems Division, Argonne National Laboratory（阿贡国家实验室运输与电力系统部门）；Computational Science Division, Argonne National Laboratory（阿贡国家实验室计算科学部门）；Argonne Leadership Computing Facility, Argonne National Laboratory（阿贡领导计算设施）；Mathematics and Computer Science Division, Argonne National Laboratory（阿贡国家实验室数学与计算机科学部门）；College of Information Sciences and Technology, Pennsylvania State University（宾夕法尼亚州立大学信息科学与技术学院）
DeepCrysTet: A Deep Learning Approach Using Tetrahedral Mesh for Predicting Properties of Crystalline Materials
SAKURA internet Inc.（樱花互联网公司）；National Institute for Materials Science (NIMS)（国立材料科学研究所）；The University of Tokyo（东京大学）；RIKEN（理化学研究所）；Kyoto University（京都大学）
G-Adaptivity: optimised graph-based mesh relocation for finite element methods
Department of Applied Mathematics；Theoretical Physics, University of Cambridge, UK；Department of Mathematical Sciences, University of Bath, UK；Department of Computer Science, University of Bath, UK；School of Computing；Mathematical Sciences, University of Leicester, UK；Laboratoire Jacques-Louis Lions, Sorbonne Universit\'e, France；Department of Computer Science；Technology, University of Cambridge, UK
G-PARC: Graph-Physics Aware Recurrent Convolutional Neural Networks for Spatiotemporal Dynamics on Unstructured Meshes
School of Data Science, University of Virginia（数据科学学院，弗吉尼亚大学）；University of Virginia（弗吉尼亚大学）；Department of Engineering Systems and Environment, University of Virginia（工程系统与环境系，弗吉尼亚大学）；Department of Mechanical and Aerospace Engineering, University of Virginia（机械与航空航天工程系，弗吉尼亚大学）；University of Iowa（爱荷华大学）
Neural P$^3$M: A Long-Range Interaction Modeling Enhancer for Geometric GNNs
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；The Chinese University of Hong Kong（香港中文大学）；University of Science and Technology of China（中国科学技术大学）；Microsoft Research AI4Science（微软研究院AI4Science）
Super-resolution of turbulent reacting flows on complex meshes using graph neural networks
FLAME Laboratory, Department of Computational and Data Sciences, Indian Institute of Science, Bengaluru, 560012, India（印度科学研究院流体动力学与能源实验室，班加罗尔）；CAPS Laboratory, Department of Mechanical and Process Engineering, ETH Zürich, 8092 Zürich, Switzerland（苏黎世联邦理工学院机械与过程工程实验室，苏黎世）；Jülich Supercomputing Centre, Forschungszentrum Jülich GmbH, Jülich, 52425, Germany（尤利希超算中心，尤利希）
Interpretable A-posteriori Error Indication for Graph Neural Network Surrogate Models
Transportation and Power Systems Division, Argonne National Laboratory（阿贡国家实验室交通与动力系统分部）；College of Information Sciences and Technology, Pennsylvania State University（宾夕法尼亚州立大学信息科学与技术学院）；Mathematics and Computer Science Division, Argonne National Laboratory（阿贡国家实验室数学与计算机科学分部）
Multi-Level GNN Preconditioner for Solving Large Scale Problems
Université Paris-Saclay（巴黎萨克雷大学）；CNRS（法国国家科学研究中心）；Inria（法国国家信息与自动化研究所）；Direction Technologie et Numerique IFP Énergies-Nouvelles（IFP新能源公司技术与数字部）；Safran Tech（赛峰科技）
Deep-Motion-Net: GNN-based volumetric organ shape reconstruction from single-view 2D projections
University of Leeds（利兹大学）；St James’s University Hospital, Leeds Teaching Hospitals NHS Trust（利兹教学医院NHS信托基金圣詹姆斯大学医院）；University of Manchester（曼彻斯特大学）；University of Sheffield（谢菲尔德大学）；University of Glasgow（格拉斯哥大学）
Scaling Kinetic Monte-Carlo Simulations of Grain Growth with Combined Convolutional and Graph Neural Networks
Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL, USA（电气与计算机工程系，佛罗里达大学，盖恩斯维尔，佛罗里达州，美国）；Northwestern University（西北大学）；Lawrence Livermore National Laboratory, Livermore, CA, United States（劳伦斯利弗莫尔国家实验室，利弗莫尔，加利福尼亚州，美国）
DUALFloodGNN: Physics-informed Graph Neural Network for Operational Flood Modeling
Department of Computer Science, School of Computing, National University of Singapore（新加坡国立大学计算机科学系）；School of Civil Engineering, Faculty of Engineering, The University of Sydney（悉尼大学土木工程学院）；Delft Institute of Applied Mathematics, Delft University of Technology（代尔夫特理工大学应用数学研究所）
Domain-Decomposed Graph Neural Network Surrogate Modeling for Ice Sheets
Institute for Computational and Mathematical Engineering, Stanford University（计算与数学工程研究所，斯坦福大学）；Department of Scientific Machine Learning, Sandia National Laboratories（科学机器学习系，桑迪亚国家实验室）；Advanced Computing, Mathematics and Data Division, Pacific Northwest National Laboratory（先进计算、数学和数据 division，太平洋西北国家实验室）；Delft Institute of Applied Mathematics, Delft University of Technology（应用数学研究所，代尔夫特理工大学）；Department of Energy Science Engineering, Stanford University（能源科学与工程系，斯坦福大学）
Momentum-Conserving Graph Neural Networks for Deformable Objects
Max Planck Institute for Informatics（马克斯·普朗克信息研究所）；ETH Zürich（苏黎世联邦理工学院）；University of Bonn（波恩大学）；Fraunhofer Institute for Algorithms and Scientific Computing（弗劳恩霍夫算法与科学计算研究所）
