Mesh-Conv: Convolution operator with mesh resolution independence for flow field modeling

Convolutional neural network (CNN) is a useful model in deep-learning and has become a promising alternative for flow field modeling due to its capability of spatial information representation. However, the standard convolution operator is only suitable for uniform Cartesian mesh, rather than non-uniform structured or unstructured mesh. In this work, a new convolution operator named Mesh-Conv is designed to allow CNN to model flow field without requiring pixelation preprocessing. This is achieved by decomposing standard convolution elements, combining the unique data type of the flow field, and introducing the concept of local weights to incorporate data structure information. The differences are clarified among the new operator, the standard convolution operator, and the graph convolution operator. In addition, new geometric features and loss functions are designed to further improve the model performance for flow field modeling. Numerical experiments show that the Mesh-Conv operator can obtain higher modeling accuracy than the standard convolution operator. The correlation coefficients of the flow fields predicted by the model are all above 0.999, and there is no checkerboard phenomenon. The Mesh-Conv operator is independent of mesh resolution to a certain extent, so its training and testing losses to the dataset with mixed mesh resolution are reduced by 63% and 55% respectively, compared with the standard convolution operator, which greatly relaxes the restriction on the data structure. Moreover, the Mesh-Conv operator is easy to be extended to most existing CNN architectures.