A hybrid deep learning framework for unsteady periodic flow field reconstruction based on frequency and residual learning

Reconstructing a complete flow field from limited sensor measurement is quite essential for state evaluation, optimization, monitoring, and control of the flow system. Unsteady periodic flow, as a widespread phenomenon in science and engineering, attracts in-depth research over decades. Deep learning has been employed in flow field reconstruction, whereas the accurate estimation for the unsteady flow field with strong nonlinearity is still difficult. To address this problem, we propose a hybrid deep learning framework that incorporates frequency and residual learning to accurately reconstruct an unsteady periodic flow field from limited sensor measurement. First, to extract the frequency features, the historical flow field data is decomposed into different modes with different frequencies named frequency modes via fast Fourier transform (FFT). Next, we construct a hybrid deep neural network framework consisting of an inverse fast Fourier transform (IFFT) block and a residual block. The IFFT block maps sensor measurements to frequency mode temporal coefficients, which are multiplied with frequency modes to recover an IFFT field. Meanwhile, the residual block adaptively generates a residual field to complement the information lost by the IFFT field. Finally, the IFFT field and residual field are combined to produce the final reconstructed flow field. We conduct numerical experiments on the unsteady periodic flow around a cylinder and transonic flow around a NACA0012 airfoil to demonstrate the feasibility and high accuracy of our proposed method. Compared to the widely used proper orthogonal decomposition (POD) and shallow decoder (SD) methods, our approach achieves at least 83.9% and 72.2% reduction in mean absolute error, respectively.