A multi-scale physics-enhanced framework for long-term unsteady flow field prediction

As an emerging approach in computational fluid dynamics, surrogate models often face challenges of long-term stability and high physical fidelity when dealing with unsteady complex flow fields. In this work, we propose a multi-scale enhanced transformer (MUSE-T) that integrates a multi-scale physical feedback gating mechanism. This mechanism operates on two levels: a physically enhanced encoder ensures instantaneous snapshots conform to the Navier–Stokes equations, while a transformer model captures temporal evolution guided by a gated feedback loop that injects spatiotemporal physical residuals into its attention layers. This dual-level integration ensures spatial accuracy and long-term stability. We demonstrate our model's superiority on the standard problem of cylinder wake. Results show that MUSE-T not only achieves reduced prediction errors compared to baseline models but also more accurately captures key flow phenomena such as vortex shedding and energy spectra. Our work establishes a new paradigm for developing physically consistent and highly accurate data-driven models for complex dynamic systems.