UCNN: A Convolutional Strategy on Unstructured Mesh
This addresses a domain-specific bottleneck in fluid mechanics simulations by enabling convolutional strategies on unstructured meshes, offering incremental improvements over existing methods.
The paper tackles the problem of applying convolutional neural networks to unstructured mesh data in fluid mechanics by proposing UCNN, which aggregates neighbor node features via a weight function. Results show UCNN is more accurate than fully-connected neural networks in modeling adjoint vectors, with specific gains demonstrated in validation and aerodynamic shape optimization test cases.
In machine learning for fluid mechanics, fully-connected neural network (FNN) only uses the local features for modelling, while the convolutional neural network (CNN) cannot be applied to data on structured/unstructured mesh. In order to overcome the limitations of FNN and CNN, the unstructured convolutional neural network (UCNN) is proposed, which aggregates and effectively exploits the features of neighbour nodes through the weight function. Adjoint vector modelling is taken as the task to study the performance of UCNN. The mapping function from flow-field features to adjoint vector is constructed through efficient parallel implementation on GPU. The modelling capability of UCNN is compared with that of FNN on validation set and in aerodynamic shape optimization at test case. The influence of mesh changing on the modelling capability of UCNN is further studied. The results indicate that UCNN is more accurate in modelling process.