In this paper, we combine a linearized iterative method with multi-scale deep neural network to compute oscillatory flows for stationary Navior-Stokes equation in complex domains. The multiscale neural network converts the high frequency components in target to low frequency components before training, thus accelerating the convergence of training of neural network for all frequencies . To solve the stationary nonlinear Navier-Stokes  equation, we introduce the idea of linearization of Navier-Stokes equation and iterative methods to treat the nonlinear convection term . Three forms of linearizations will be considered. First we will conduct a benchmark problem of the linearized schemes in comparison with schemes based directly on the nonlinear PDE. Then, a Navier Stokes flow with high frequency components in a 2-D domain with a hole are learned by the linearized multiscale deep multiscale neural network . The results show that multiscale deep neural network combining with the linearized schemes can be trained fast and accurately.
In this paper, we present linearized learning methods to accelerate the convergence of training for stationary nonlinear Navier-Stokes equations . To solve the stationary nonlinear Navier-Stokes (NS) equation, we integrate the procedure of linearization of the nonlinear convection term in the NS equation into the training process of multi-scale deep neural network approximation of the NS solution. Four forms of linearizations are considered. After a benchmark problem , we solve the highly oscillating stationary flows utilizing the proposed linearized learning with multi-scale neural network for complex domains . The results show that multiscale deep neural network combining with the linearized schemes can be trained fast and accurately.
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combine a linearized iterative method with multi-scale deep neural network to compute oscillatory flows for stationary Navior-Stokes equation in complex domains. The multiscale neural network converts the high frequency components in target to low frequency components before training, thus accelerating the
present linearized learning methods to accelerate the
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of neural network for all frequencies
for stationary nonlinear Navier-Stokes equations
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(NS)
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introduce the idea
integrate the procedure
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Navier-Stokes equation and iterative methods to treat
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. Three
in the NS equation into the training process of multi-scale deep neural network approximation of the NS solution. Four
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will be considered. First we will conduct
are considered. After
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of the linearized schemes in comparison with schemes based directly on the nonlinear PDE. Then, a Navier Stokes flow with high frequency components in a 2-D domain with a hole are learned by the linearized multiscale deep multiscale neural network
, we solve the highly oscillating stationary flows utilizing the proposed linearized learning with multi-scale neural network for complex domains