Physics-Driven Learning of the Steady Navier-Stokes Equations Using Deep Convolutional Neural Networks (Communications in Computational Physics, 2022)
Recently, physics-driven deep learning methods have shown particularpromise for the prediction of physical fields, especially to reduce the dependency onlarge amounts of pre-computed training data. In this work, we target the physics-driven learning of complex flow fields with high resolutions. We propose the use ofConvolutional neural networks (CNN) based U-net architectures to efficiently representand reconstruct the input and output fields, respectively. By introducing Navier-Stokesequations and boundary conditions into loss functions, the physics-driven CNN is designed to predict corresponding steady flow fields directly. In particular, this preventsmany of the difficulties associated with approaches employing fully connected neuralnetworks. Several numerical experiments are conducted to investigate the behaviorof the CNN approach, and the results indicate that a first-order accuracy has beenachieved. Specifically for the case of a flow around a cylinder, different flow regimescan be learned and the adhered “twin-vortices” are predicted correctly. The numerical results also show that the training for multiple cases is accelerated significantly,especially for the difficult cases at low Reynolds numbers, and when limited referencesolutions are used as supplementary learning targets.