Physics-assisted multi-scale convolutional autoencoder for turbulence reduced-order modeling

Reduced-order modeling techniques, including the proper orthogonal decomposition and the dynamic mode decomposition, have been widely applied in unsteady flow rather than in fully developed turbulent flows, but these techniques are faced with challenges in simulating turbulence with high degrees of freedom and complex nonlinear interactions. One possible approach is to utilize a series of neural networks, such as autoencoders, to reduce the dimensionality of unsteady flows. This study began with combining a multi-scale convolutional autoencoder with a convolutional block attention module to extract the main features of turbulence. Then, physical constraint terms were added to the loss function to improve the accuracy of feature extraction. Finally, flow data was restored with potential physical properties. Forced isotropic turbulence with Reλ=418 and turbulent channel flow with Reτ=1000 were employed to test the model's performance, and the numerical results verified that the model can accurately extract the main features of turbulence and has an excellent ability to restore the flow data.