With this study we investigate the accuracy of deep learning models for the inference of Reynolds-Averaged Navier-Stokes solutions. We focus on a modernized U-net architecture, and evaluate a large number of trained neural networks with respect to their accuracy for the calculation of pressure and velocity distributions. In particular, we illustrate how training data size and the number of weights influence the accuracy of the solutions. With our best models we arrive at a mean relative pressure and velocity error of less than 3% across a range of previously unseen airfoil shapes. In addition all source code is publicly available in order to ensure reproducibility and to provide a starting point for researchers interested in deep learning methods for physics problems. While this work focuses on RANS solutions, the neural network architecture and learning setup are very generic, and applicable to a wide range of PDE boundary value problems on Cartesian grids.

本研究探讨了深度学习模型在推断雷诺平均Navier-Stokes方程的解中精度的问题，着重于现代化的U形网络架构，并评估了大量经过训练的神经网络，特别是说明了训练数据大小和权重数量对解的精度的影响。结论表明，通过我们的最佳模型，我们对于一系列之前从未见过的翼型形状得到平均相对压力和速度误差小于3％。此外，为确保可重复性，并为对物理问题深度学习方法感兴趣的研究人员提供一个起点，我们公开了所有源代码。虽然本研究集中于RANS解，但神经网络架构和学习设置非常通用，并适用于笛卡尔网格上广泛范围的偏微分方程边界值问题。

用于翼型气动流混合雷诺平均-纳维尔-斯托克斯模拟的深度学习方法