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...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.展开更多
文摘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.
