Before revision:  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 .
After revision:  First we will conduct a benchmark problem , we solve the highly oscillating stationary flows utilizing the proposed linearized learning with multi-scale neural network for complex domains .