UCNN: A Convolutional Strategy on Unstructured Mesh

TL;DR

This paper introduces UCNN, a novel convolutional neural network designed for unstructured mesh data in fluid mechanics, demonstrating improved accuracy over traditional FNNs and robustness to mesh variations.

Contribution

The paper proposes UCNN, a new convolutional strategy for unstructured meshes, enabling effective feature aggregation and improved modeling in fluid mechanics applications.

Findings

UCNN outperforms FNN in modeling accuracy.

UCNN is effective in aerodynamic shape optimization.

Mesh variations have limited impact on UCNN performance.

Abstract

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.