Efficient Vision Transformer-based Surrogate for Scalable Pressure Prediction in Incompressible Turbulent Flows

Pressure estimation in turbulent flows is crucial to model and understand the evolution of turbulence, boundary-layer behavior, and energy distribution. Unlike compressible flow, pressure is not a thermodynamic state variable in incompressible flows, rather pressure acts as a kinematic constraint governed by the Pressure Poisson Equation (PPE) and keeps the flow divergence-free. The PPE is generally solved via traditional numerical solvers, which are often prohibitively expensive for high-resolution pressure fields. Advanced deep learning approaches offer a compelling alternative; however, data-driven pressure prediction remains challenging due to the high dimensionality and inherent multiscale dynamics of turbulent flows. Conventional machine learning architectures typically impose strong locality assumptions and fixed receptive fields, limiting their ability to capture long-range pressure interactions and generalize beyond training distribution. To address these challenges, we adopt a Vision Transformer (ViT)-based architecture that explicitly models nonlocal dependencies through self-attention and enables patch-based representations suited for multiscale turbulence. We propose a hybrid loss function that incorporates a pressure-gradient consistency loss to better enforce physically meaningful pressure fluctuations. While effective, a consequential downside of standard ViT is that the computational cost scales up quadratically as the number of patches grows, hindering scalability to large flows. We therefore introduce a physics-guided adaptive patching mechanism that dynamically decides the patch size based on the richness of information and predefined reduced sequence length, substantially improving computational efficiency. Experimental results on oceanic incompressible stratified turbulence demonstrate that the designed ViT framework accurately predicts turbulent pressure fields, and that the adaptive patching-based ViT model achieves competitive accuracy at a significantly reduced computation cost. These results highlight the potential of physics-guided scalable transformer models for pressure prediction across diverse application domains, including aeroacoustics, atmospheric science, and oceanic turbulence where incompressible flow arises.