Abstract Despite the significant breakthrough of neural networks in the last few years, their spreading in the field of computational fluid dynamics is very recent, and many applications remain to explore. In this paper, we explore the drag prediction capabilities of convolutional neural networks for laminar, low-Reynolds number flows past arbitrary 2D shapes. A set of random shapes exhibiting a rich variety of geometrical features is built using Bezier curves. The efficient labelling of the shapes is provided using an immersed method to solve a unified Eulerian formulation of the Navier-Stokes equation. The network is then trained and optimized on the obtained dataset, and its predictive efficiency assessed on several real-life shapes, including NACA airfoils.

中文翻译：

---

用于预测低雷诺数层流中任意 2D 形状阻力的监督神经网络

摘要 尽管神经网络在过去几年取得了重大突破，但它们在计算流体动力学领域的传播却是最近的，许多应用仍有待探索。在本文中，我们探索了卷积神经网络对层流、低雷诺数流过任意 2D 形状的阻力预测能力。一组具有丰富几何特征的随机形状是使用贝塞尔曲线构建的。使用浸入式方法来求解 Navier-Stokes 方程的统一欧拉公式，可以提供对形状的有效标记。然后在获得的数据集上训练和优化网络，并在几种真实形状（包括 NACA 翼型）上评估其预测效率。