Progressive multi-scale reduced-order modeling method for accurate unsteady flow prediction

Reduced-order models based on deep learning provide an efficient solution for predicting nonlinear flow fields in aerospace and marine engineering. However, existing methods often neglect the multi-scale characteristics of unsteady flow fields, which reduces the prediction accuracy. A progressive multi-scale reduced-order modeling method (PMS-ROM) based on an enhanced three-dimensional U-shaped convolutional neural network (3D U-Net) is proposed in this study. The training data containing features at different scales is constructed by proper orthogonal decomposition. A mixed loss function is introduced to optimize the learning ability of the model on different features. The PMS-ROM is evaluated by the flow problem around a cylinder. The results show that its predictions closely match computational fluid dynamics calculations. Compared to a standard encoder–propagator–decoder network, PMS-ROM method improves the prediction accuracy by over 50% and maintains reliable performance under Gaussian noise levels of up to 30%. It demonstrates the superior accuracy and robustness.