Stacked Deep Learning Models for Fast Approximations of Steady-State Navier–Stokes Equations for Low Re Flow

Abstract

Computational fluid dynamics (CFD) simulations are broadly used in many engineering and physics fields. CFD requires the solution of the Navier–Stokes (N-S) equations under complex flow and boundary conditions. However, applications of CFD simulations are computationally limited by the availability, speed, and parallelism of high-performance computing. To address this, machine learning techniques have been employed to create data-driven approximations for CFD to accelerate computational efficiency. Unfortunately, these methods predominantly depend on large labeled CFD datasets, which are costly to procure at the scale required for robust model development. In response, we introduce a weakly supervised approach that, through a multichannel input capturing boundary and geometric conditions, solves steady-state N-S equations. Our method achieves state-of-the-art results without relying on labeled simulation data, instead using a custom data-driven and physics-informed loss function and small-scale solutions to prime the model for solving the N-S equations. By training stacked models, we enhance resolution and predictability, yielding high-quality numerical solutions to N-S equations without hefty computational demands. Remarkably, our model, being highly adaptable, produces solutions on a 512 × 512 domain in a swift 7 ms, outpacing traditional CFD solvers by a factor of 1,000. This paves the way for real-time predictions on consumer hardware and Internet of Things devices, thereby boosting the scope, speed, and cost-efficiency of solving boundary-value fluid problems.