FV-FluidAttentionNet: A Label-Free Physics-Informed Autoencoder with Finite-Volume Discretization for Rapid Navier-Stokes Solutions

We present FV-FluidAttentionNet, a novel physics-informed autoencoder with attention mechanism for solving Navier-Stokes equations. This label-free surrogate model integrates finite-volume discretization within its computational graph, enabling fast GPU-based calculations of PDE residuals. Our approach significantly reduces computational time—by a factor of 1000 compared to conventional CFD solvers—while maintaining high accuracy. FV-FluidAttentionNet demonstrates exceptional performance in solving steady, incompressible Navier-Stokes equations for various scenarios, including 3D lid-driven cavity flow and flow past a cylinder at different Reynolds numbers. Notably, it excels in both interpolation and extrapolation, accurately predicting flow fields for non-dimensional parameters outside the training data. This generalization capability, combined with its speed and accuracy, positions FV-FluidAttentionNet as a transformative tool in computational fluid dynamics, offering potential for rapid, adaptive, and physically consistent simulations across diverse fluid dynamics applications.