We focus on a convolutional neural network (CNN), which has recently been utilized for fluid flow analyses, from the perspective on the influence of various operations inside it by considering some canonical regression problems with fluid flow data. We consider two types of CNN-based fluid flow analyses: (1) CNN metamodeling and (2) CNN autoencoder. For the first type of CNN with additional scalar inputs, which is one of the common forms of CNN for fluid flow analysis, we investigate the influence of input placements in the CNN training pipeline. As an example, estimation of drag and lift coefficients of an inclined flat plate and two side-by-side cylinders in laminar flows is considered. For the example of flat plate wake, we use the chord Reynolds number \(\hbox {Re}_\mathrm{c}\) and the angle of attack \(\alpha \) as the additional scalar inputs to provide the information on the complexity of wake. For the wake interaction problem comprising flows over two side-by-side cylinders, the gap ratio and the diameter ratio are utilized as the additional inputs. We find that care should be taken for the placement of additional scalar inputs depending on the problem setting and the complexity of flows that users handle. We then discuss the influence of various parameters and operations on the CNN performance, with the utilization of autoencoder (AE). A two-dimensional decaying homogeneous isotropic turbulence is considered for the demonstration of AE. The results obtained through the AE highly rely on the decaying nature. Investigation on the influence of padding operation at a convolutional layer is also performed. The zero padding shows reasonable ability compared to other methods which account for the boundary conditions assumed in the numerical data. Moreover, the effect of the dimensional reduction/extension methods inside CNN is also examined. The CNN model is robust against the difference in dimension reduction operations, while it is sensitive to the dimensional extension methods. The findings of this paper will help us better design a CNN architecture for practical fluid flow analysis.

我们专注于最近被用于流体流动分析的卷积神经网络 (CNN)，通过考虑流体流动数据的一些典型回归问题，从其内部各种操作的影响的角度来看。我们考虑两种基于 CNN 的流体流动分析：（1）CNN 元建模和（2）CNN 自动编码器。对于具有附加标量输入的第一类 CNN，这是 CNN 用于流体流动分析的常见形式之一，我们研究了 CNN 训练管道中输入位置的影响。例如，考虑了层流中倾斜平板和两个并排圆柱体的阻力和升力系数的估计。对于平板尾流的例子，我们使用弦雷诺数\(\hbox {Re}_\mathrm{c}\)和攻角\（\α \）作为额外的标量输入，以提供有关唤醒复杂性的信息。对于包括流过两个并排圆柱体的尾流相互作用问题，间隙比和直径比被用作附加输入。我们发现，根据问题设置和用户处理的流程的复杂性，应该注意放置额外的标量输入。然后，我们讨论了各种参数和操作对 CNN 性能的影响，利用自动编码器（AE）。二维衰减均匀各向同性湍流被考虑用于演示 AE。通过 AE 获得的结果高度依赖于衰减性质。还对卷积层的填充操作的影响进行了调查。与考虑数值数据中假设的边界条件的其他方法相比，零填充显示出合理的能力。此外，还检查了 CNN 内部降维/扩展方法的效果。CNN 模型对降维操作的差异具有鲁棒性，而对维扩展方法很敏感。本文的发现将帮助我们更好地设计用于实际流体流动分析的 CNN 架构。