Convolutional neural networks for fluid flow analysis: toward effective metamodeling and low dimensionalization

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 Re-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.