A physics-embedded Transformer-CNN architecture for data-driven turbulence prediction and surrogate modeling of high-fidelity fluid dynamics

Turbulence modeling poses significant challenges due to its nonlinear, multiscale nature. Classical methods like Reynolds-Averaged Navier–Stokes and Large Eddy Simulation often rely on empirical closures, which limit their accuracy in complex flows. This study aims to propose a hybrid model that integrates convolutional neural networks for capturing local spatial patterns with Transformer-based attention modules to model long-range dependencies. The architecture is informed by the Navier–Stokes equations and incorporates divergence-free constraints to preserve physical fidelity. The model is trained and evaluated on direct numerical simulation datasets representing 2D turbulence and turbulent channel flows. The model achieved up to 40 % reduction in prediction error compared to CNN and RNN baselines. It accurately reproduced key flow structures and energy spectra, showing strong agreement with DNS outputs. The hybrid architecture demonstrated stable long-term predictions and matched statistical flow properties over extended time horizons. For steady flows, it corrected RANS-predicted biases in mean velocity profiles with near-exact reconstruction. The results validate the effectiveness of combining physics-informed learning with deep neural architectures. The proposed framework offers a computationally efficient alternative to traditional turbulence models while retaining accuracy, marking a promising advancement in data-driven fluid mechanics.