Fast flow field prediction based on E(2)-equivariant steerable convolutional neural networks

In the field of flow field reconstruction, traditional deep learning models predominantly rely on standard convolutions, but their predictive accuracy remains limited. To address this issue, we explore the potential of E(2)-equivariant convolutions to enhance the predictive accuracy of deep learning models for fast flow field prediction. Unlike conventional convolutions, E(2)-equivariant convolutions offer a richer representation capability by better capturing geometric and structural information. Our neural network integrates an attention mechanism that leverages the signed distance function (SDF) to encode geometric details and an indicator matrix to incorporate boundary conditions. The model predicts velocity and pressure fields as outputs. We conducted experiments specifically targeting non-uniform steady laminar flows, and the results show a 16.1% reduction in overall error compared to models based on traditional convolutions while maintaining high efficiency. These findings indicate that E(2)-equivariant convolution, coupled with an attention mechanism, significantly improves flow field prediction by focusing on critical information and better representing complex geometries.