A physics-integrated attention model with dynamic weighting for rapid and precise turbulent flow prediction in variable geometries

Achieving high-precision and efficient prediction of turbulent flow fields presents a significant challenge for the rapid design of complex flow channels. Traditional turbulent flow field calculation methods require solving the Navier–Stokes equations, which are computationally intensive and time-consuming. Other than the traditional method, a novel fast prediction method of two-dimensional flow is proposed in this study based on a deep attention network integrating physical information. First, the geometric information of flow channels is extracted based on a series of grayscale images, which are then embedded and input into a transformer encoder. The geometric parameters obtained from the transformer encoder, along with the Reynolds number, flow field coordinates, and distance field, are input into a multilayer perceptron to predict the flow field. To enhance the network's physical interpretability, a physical loss function is incorporated into the network. Additionally, a dynamic weight strategy is employed to balance the interaction between data loss terms and physical loss terms. Extensive quantitative comparison between the predicted and numerical simulation results of the back-step vortex field with varying geometric structures shows that 80% of data points have an absolute relative error below 0.02. The correlation coefficient between the predicted and computational fluid dynamics (CFD) values is greater than 0.97, with near-wall pressure values closely matching the CFD results. Additionally, the model requires no manual weight adjustments, and dynamic weighting reduces training losses while improving performance.