@Article{CiCP-32-3,
author = {Ma, Hao and Zhang, Yuxuan and Thuerey, Nils and Xiangyu, Hu and Oskar, J., Haidn},
title = {Physics-Driven Learning of the Steady Navier-Stokes Equations Using Deep Convolutional Neural Networks},
journal = {Communications in Computational Physics},
year = {2022},
volume = {32},
number = {3},
pages = {715--736},
abstract = {<p style="text-align: justify;">Recently, physics-driven deep learning methods have shown particular
promise for the prediction of physical fields, especially to reduce the dependency on
large 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 of
Convolutional neural networks (CNN) based U-net architectures to efficiently represent
and reconstruct the input and output fields, respectively. By introducing Navier-Stokes
equations and boundary conditions into loss functions, the physics-driven CNN is designed to predict corresponding steady flow fields directly. In particular, this prevents
many of the difficulties associated with approaches employing fully connected neural
networks. Several numerical experiments are conducted to investigate the behavior
of the CNN approach, and the results indicate that a first-order accuracy has been
achieved. Specifically for the case of a flow around a cylinder, different flow regimes
can 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 reference
solutions are used as supplementary learning targets.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2021-0146},
url = {https://global-sci.com/article/79479/physics-driven-learning-of-the-steady-navier-stokes-equations-using-deep-convolutional-neural-networks}
}