Graph-based next-step prediction models have recently been very successful in modeling complex high-dimensional physical systems on irregular meshes. However, due to their short temporal attention span, these models suffer from error accumulation and drift. In this paper, we propose a new method that captures long-term dependencies through a transformer-style temporal attention model. We introduce an encoder-decoder structure to summarize features and create a compact mesh representation of the system state, to allow the temporal model to operate on a low-dimensional mesh representations in a memory efficient manner. Our method outperforms a competitive GNN baseline on several complex fluid dynamics prediction tasks, from sonic shocks to vascular flow. We demonstrate stable rollouts without the need for training noise and show perfectly phase-stable predictions even for very long sequences. More broadly, we believe our approach paves the way to bringing the benefits of attention-based sequence models to solving high-dimensional complex physics tasks.
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）
Parametric Interpolation of Dynamic Mode Decomposition for Predicting Nonlinear Systems
Department of Electrical and Computer Engineering, The Ohio State University（俄亥俄州立大学电气与计算机工程系）；ElectroScience Laboratory, The Ohio State University（俄亥俄州立大学电科学实验室）；Department of Mechanical and Aerospace Engineering, The Ohio State University（俄亥俄州立大学机械与航空航天工程系）；SLAC National Accelerator Laboratory, Stanford University（斯坦福大学SLAC国家加速器实验室）
