This paper presents an approach for the prediction of incompressible laminar steady flow fields over various geometry types. In conventional approaches of computational fluid dynamics (CFD), flow fields are obtained by solving model equations on computational grids, which is in general computationally expensive. Based on the ability of neural networks to intuitively identify and approximate nonlinear physical relationships, the proposed method makes it possible to eliminate the explicit implementation of model equations such as the Navier–Stokes equations. Moreover, it operates without iteration or spatial discretization of the flow problem. The method is based on the combination of a minimalistic multilayer perceptron (MLP) architecture and a radial-logarithmic filter mask (RLF). The RLF acts as a preprocessing step and its purpose is the spatial encoding of the flow guiding geometry into a compressed form, that can be effectively interpreted by the MLP. The concept is applied on internal flows as well as on external flows (e.g. airfoils and car shapes). In the first step, datasets of flow fields are generated using a CFD-code. Subsequently the neural networks are trained on defined portions of these datasets. Finally, the trained neural networks are applied on the remaining unknown geometries and the prediction accuracy is evaluated. Dataset generation, neural network implementation and evaluation are carried out in MATLAB. To ensure reproducibility of the results presented here, the trained neural networks and sample applications are made available for free download and testing.

本文提出了一种预测各种几何类型上不可压缩层流稳定流场的方法。在计算流体动力学（CFD）的常规方法中，通过在计算网格上求解模型方程来获得流场，这通常在计算上是昂贵的。基于神经网络直观地识别和近似非线性物理关系的能力，所提出的方法使得消除诸如Navier–Stokes方程等模型方程的显式实现成为可能。此外，它的运行无需对流动问题进行迭代或空间离散。该方法基于简约的多层感知器（MLP）体系结构和径向对数过滤器蒙版（RLF）的组合。RLF充当预处理步骤，其目的是将导流几何图形空间编码为压缩形式，MLP可以有效地对其进行解释。该概念适用于内部流动以及外部流动（例如，机翼和汽车形状）。第一步，使用CFD代码生成流场的数据集。随后，在这些数据集的定义部分上训练神经网络。最后，将训练后的神经网络应用于剩余的未知几何形状，并评估预测精度。数据集生成，神经网络实现和评估均在MATLAB中进行。为了确保此处显示的结果的可重复性，经过培训的神经网络和示例应用程序可免费下载和测试。