Accelerated Elliptical PDE Solver for Computational Fluid Dynamics Based on Configurable U-Net Architecture: Analogy to V-Cycle Multigrid  

作　　者：Kiran Bhaganagar David Chambers 

机构地区：[1]Laboratory of Turbulence,Sensing and Intelligence Systems,Department of Mechanical Engineering,University of Texas,San Antonio 78249,USA [2]Intelligence Systems Division,Southwest Research Institute,San Antonio 78238,USA

出　　处：《Machine Intelligence Research》2025年第2期324-336,共13页机器智能研究(英文版)

摘　　要：A configurable U-Net architecture is trained to solve the multi-scale elliptical partial differential equations.The motivation is to improve the computational cost of the numerical solution of Navier-Stokes equations–the governing equations for fluid dynamics.Building on the underlying concept of V-Cycle multigrid methods,a neural network framework using U-Net architecture is optimized to solve the Poisson equation and Helmholtz equations–the characteristic form of the discretized Navier-Stokes equations.The results demonstrate the optimized U-Net captures the high dimensional mathematical features of the elliptical operator and with a better convergence than the multigrid method.The optimal performance between the errors and the FLOPS is the(3,2,5)case with 3 stacks of UNets,with 2 initial features,5 depth layers and with ELU activation.Further,by training the network with the multi-scale synthetic data the finer features of the physical system are captured.

关 键 词：Configurable U-Net architecture neural network methods for elliptical equations multi-scale partial differential equations Poisson and Helmholtz equation solvers computational fluid dynamics solutions. 

分 类 号：O241.82[理学—计算数学]