We present a novel deep learning framework for flow field predictions in irregular domains when the solution is a function of the geometry of either the domain or objects inside the domain. Grid vertices in a computational fluid dynamics (CFD) domain are viewed as point clouds and used as inputs to a neural network based on the PointNet architecture, which learns an end-to-end mapping between spatial positions and CFD quantities. Using our approach, (i) the network inherits desirable features of unstructured meshes (e.g., fine and coarse point spacing near the object surface and in the far field, respectively), which minimizes network training cost; (ii) object geometry is accurately represented through vertices located on object boundaries, which maintains boundary smoothness and allows the network to detect small changes between geometries; and (iii) no data interpolation is utilized for creating training data; thus accuracy of the CFD data is preserved. None of these features are achievable by extant methods based on projecting scattered CFD data into Cartesian grids and then using regular convolutional neural networks. Incompressible laminar steady flow past a cylinder with various shapes for its cross section is considered. The mass and momentum of predicted fields are conserved. We test the generalizability of our network by predicting the flow around multiple objects as well as an airfoil, even though only single objects and no airfoils are observed during training. The network predicts the flow fields hundreds of times faster than our conventional CFD solver, while maintaining excellent to reasonable accuracy.
Yale University（耶鲁大学）；NC State University（北卡罗来纳州立大学）；Halıcıoğlu Data Science Institute, UC San Diego（加州大学圣地亚哥分校Halıcıoğlu数据科学研究所）
Graph signal processing (GSP) is an important methodology for studying data residing on irregular structures. As acquired data is increasingly taking the form of multi-way tensors, new signal processing tools are needed to maximally utilize the multi-way structure within the data. In this paper, we review modern signal processing frameworks generalizing GSP to multi-way data, starting from graph signals coupled to familiar regular axes such as time in sensor networks, and then extending to general graphs across all tensor modes. This widely applicable paradigm motivates reformulating and impro…
Neuroscience Inspired Graph Operators Towards Edge-Deployable Virtual Sensing for Irregular Geometries
Grainger College of Engineering, Nuclear, Plasma & Radiological Engineering Department, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校格拉inger工程学院，核物理与等离子体工程系）；Department of Applied Mechanics, Indian Institute of Technology Delhi（印度理工学院德里应用力学系）；Yardi School of Artificial Intelligence, Indian Institute of Technology Delhi（印度理工学院德里人工智能学院）；National Center for Supercomputing Applications（国家超级计算应用中心）
GRIFDIR: Graph Resolution-Invariant Diffusion Models over Irregular Domains
University of Cambridge（剑桥大学）；Technical University of Denmark（丹麦技术大学）；Simon Fraser University（西蒙弗雷泽大学）；Helmholtz Imaging（亥姆霍兹成像中心）；Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器研究所）
Meshless solutions of PDE inverse problems on irregular geometries
School of Engineering and Applied Sciences, Harvard University, Cambridge MA 02138（工程与应用科学学院，哈佛大学，康科德马萨诸塞州02138）；School of Engineering（工程学院）；Applied Sciences, Harvard University, Cambridge MA 02138（应用科学，哈佛大学，康科德马萨诸塞州02138）；Department of Physics, Harvard University, Cambridge MA 02138（物理系，哈佛大学，康科德马萨诸塞州02138）
Numerical simulators are essential tools in the study of natural fluid-systems, but their performance often limits application in practice. Recent machine-learning approaches have demonstrated their ability to accelerate spatio-temporal predictions, although, with only moderate accuracy in comparison. Here we introduce MultiScaleGNN, a novel multi-scale graph neural network model for learning to infer unsteady continuum mechanics in problems encompassing a range of length scales and complex boundary geometries. We demonstrate this method on advection problems and incompressible fluid dynamics,…
The ubiquity of fluids in the physical world explains the need to accurately simulate their dynamics for many scientific and engineering applications. Traditionally, well established but resource intensive CFD solvers provide such simulations. The recent years have seen a surge of deep learning surrogate models substituting these solvers to alleviate the simulation process. Some approaches to build data-driven surrogates mimic the solver iterative process. They infer the next state of the fluid given its previous one. Others directly infer the state from time input. Approaches also differ in t…
A Synergistic Framework Leveraging Autoencoders and Generative Adversarial Networks for the Synthesis of Computational Fluid Dynamics Results in Aerofoil Aerodynamics
