Prediction of internal and external flow with sparse convolution neural network: A computationally effective reduced-order model

Abstract

This paper presents a novel reduced-order model for internal and external flow field estimations based on a sparse convolution neural network. Since traditional convolution neural network requires “rectangular” matrixes as input, the convolutional operation is computationally inefficient when applied to these problems with input matrix having sparse information. In our approach, we innovatively introduce a sparse convolution neural network (SCNN) to collect spatial information on geometries that are inherently sparse, e.g., the flow in thin pipelines in a much larger domain or the pipelines with random branches. Different from the traditional convolution neural network (CNN) model, the SCNN only collects features from areas with flow information for both the input matrix and each convolutional layer, which not only reduces the consumption of computational resources but also significantly increases network attention to flow area. The model learns the mapping relationship between geometries and the physical field of fluid flow, and the spatial positions of geometry are represented using the nearest wall signed distance function. The proposed SCNN model has the promising adaptability to arbitrary geometry and less computational resource cost compared to the traditional CNN model: the mean error of the SCNN is less than 5.4% (while the CNN is 7.1%) for the internal flow and less than 6.5% (while the CNN is 8.1%) for the external flow. Moreover, the SCNN has 72% less GPU resource usage and 52% less random access memory cost than the CNN for internal flow. For the first time, our framework introduces the sparse convolution network to flow field prediction, and the SCNN shows outstanding performance on prediction accuracy and computational resource saving for the flow problems with a sparse input information.