Physics-informed multi-scale spatiotemporal learning for transient incompressible flow prediction
Data-driven learning provides a promising route for accelerating computational fluid dynamics, yet transient flow prediction remains challenging because models must simultaneously capture evolving temporal dynamics and cross-scale spatial structures while generalizing across geometries and operating conditions. In this work, we study one-step-ahead prediction of two-dimensional incompressible transient flows from historical snapshots and propose Multi-Scale Spatiotemporal Flow (MuST-Flow), a physics-informed multi-scale spatiotemporal network for recurrent forecasting of velocity and pressure fields. The central idea of MuST-Flow is to couple cross-scale feature extraction with physical regularization, enabling the model to better resolve localized high-gradient flow structures while maintaining physically consistent evolution. Specifically, MuST-Flow adopts a multi-scale spatiotemporal convolutional design with dilated receptive fields to learn hierarchical flow representations and incorporates a hybrid loss derived from the residuals of the incompressible Navier–Stokes equations to encourage mass and momentum consistency during training. To evaluate generalization beyond fixed configurations, the proposed method is assessed on transient hydrofoil flow data under cross-geometry testing with varied operating conditions. Experimental results show that MuST-Flow achieves the lowest mean absolute error, highest structural similarity, and lowest speed and velocity-direction errors among both generic spatiotemporal prediction baselines and flow-oriented neural-operator baselines, while maintaining competitive divergence and Navier–Stokes residuals. These results demonstrate its effectiveness as an efficient surrogate modeling framework for two-dimensional incompressible transient flow prediction.