A multigrid-based super-resolution convolutional neural network for multi-physical fields

A novel convolutional neural network-based super-resolution (SR) method was proposed to accurately predict high-resolution flow fields from coarse-grid computational fluid dynamics (CFD) results. To mitigate boundary artifacts caused by transposed convolution, a Boundary Compensated Module was developed, ensuring input conservation by balancing the “Upper Layer Contribution Number.” A Two-step Preprocessing Scheme combined with the nondimensionalized mean square error was introduced, which effectively tackled the issues associated with “multi-physical variables” and “wide operating conditions.” Furthermore, a multigrid-based super-resolution convolutional neural network was developed, incorporating a three-stage progressive upsampling process with hierarchical loss and regularization. The model enabled efficient reconstruction under conditions of “high SR factor” and “multi-physical variables.” The effectiveness of the proposed method was validated across four representative benchmark cases (Backward-Facing Step Flow, Lid-Driven Cavity Flow, Supersonic Flow, and Swirling Jet Flow), which demonstrated that the proposed method reduces L2 errors by approximately 50% compared with existing models. The method achieved roughly two orders of magnitude of computational speedup, demonstrating strong engineering viability as a surrogate for high-fidelity CFD simulations.