A convolutional strategy on unstructured mesh for the adjoint vector modeling

In machine learning for fluid mechanics, the fully connected neural network (FNN) only uses local features for modeling, while the convolutional neural network (CNN) cannot be applied to data on structured/unstructured mesh. In order to overcome the limitations of the FNN and CNN, the unstructured convolutional neural network (UCNN) is proposed, which aggregates and effectively exploits the features of neighbor nodes through the weight function. Adjoint vector modeling is taken as the task to study the performance of the UCNN. The mapping function from flow-field features to the adjoint vector is constructed through efficient parallel implementation on graphics processing unit (GPU). The modeling capability of the UCNN is compared with that of the FNN on the validation set and in aerodynamic shape optimization in the test case. The influence of mesh changing on the modeling capability of the UCNN is further studied. The results indicate that the UCNN is more accurate in the modeling process.