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.

翻译：在本文中,我们介绍了加速固定式非线性Navier-Stokes方程式培训趋同的线性学习方法。为了解决固定式非线性Navier-Stokes(NS)方程式问题,我们将非线性对流术语在NS方程式中的线性化程序纳入NS解决方案的多尺度深神经网络近似化培训过程。考虑了四种线性化形式。在一个基准问题之后,我们利用拟议的线性学习与复杂域的多尺度神经网络来解决高度振动的固定性流动。结果显示,可以快速和准确地培训与线性计划相结合的多级深层神经网络。