Filter membranes are the core components of the solid–liquid separation equipment, and their control over particulate pollutants directly determines the effective operation of the system. The feeding of the balaenid whales, acting as an “oral filter,” provides new technical ideas for the design of traditional filter membranes. This study proposes a 3-input, 9-output UNet deep learning framework and applies it to rapid flow field prediction in patterned baleen membranes of balaenid whales during filter feeding, named UNet-BaleenCFD. The datasets are obtained through computational fluid dynamics (CFD) simulations combined with linear interpolation, and the model is validated for the effectiveness against the revised theoretical model. To account for the differences in units and magnitudes of velocity and pressure, dimensionless velocity and pressure values are calculated in the loss function. Compared to the traditional CFD, UNet-BaleenCFD can accelerate by three orders of magnitude. Additionally, the predictions made by UNet-BaleenCFD are in good agreement with the results from CFD, indicating that UNet-BaleenCFD is a promising method for predicting flow fields in filter channels. This study can provide effective theoretical guidance for the development of new filter membranes.