UTransNet: An efficient hybrid architecture of convolutional neural networks and transformer for the approximation of non-uniform steady laminar flow

Computational fluid dynamics (CFD) is crucial in various fields but is computationally expensive and time-consuming, largely due to the complex nonlinear partial differential terms that complicate its equations. A data-driven surrogate model integrating Convolutional Neural Networks and Transformer, named UTransNet, is proposed to effectively approximate solutions for a two-dimensional incompressible non-uniform steady laminar flow that have traditionally been solved by mesh-dependent numerical methods. The encoder module, based on depthwise separable convolution, extracts the local geometric features within the flow region. Subsequently, the attention mechanism of the Transformer integrates these features, enabling the model to capture global information. Utilizing the decoder module constructed by deconvolution, the model restores the dimension of the flow region. The integration of local feature extraction and global perception capabilities enables the UTransNet to predict the velocity and pressure fields more effectively. Experimental results show that the total mean square error is reduced by about a factor of 12 compared with previous works. Also, the proposed model achieves a speedup of over 3 orders of magnitude over the CFD solver on Central Processing Unit (CPU) or Graphics Processing Unit. Qualitative and quantitative analyses reveal a high level of similarity between the predicted and ground-truth data.