Stacked Generative Machine Learning Models for Fast Approximations of Steady-State Navier-Stokes Equations

Abstract

Computational fluid dynamics (CFD) simulations are broadly applied in engineering and physics. A standard description of fluid dynamics requires solving the Navier-Stokes (N-S) equations in different flow regimes. However, applications of CFD simulations are computationally-limited by the availability, speed, and parallelism of high-performance computing. To improve computational efficiency, machine learning techniques have been used to create accelerated data-driven approximations for CFD. A majority of such approaches rely on large labeled CFD datasets that are expensive to obtain at the scale necessary to build robust data-driven models. We develop a weakly-supervised approach to solve the steady-state N-S equations under various boundary conditions, using a multi-channel input with boundary and geometric conditions. We achieve state-of-the-art results without any labeled simulation data, but using a custom data-driven and physics-informed loss function by using and small-scale solutions to prime the model to solve the N-S equations. To improve the resolution and predictability, we train stacked models of increasing complexity generating the numerical solutions for N-S equations. Without expensive computations, our model achieves high predictability with a variety of obstacles and boundary conditions. Given its high flexibility, the model can generate a solution on a 64 x 64 domain within 5 ms on a regular desktop computer which is 1000 times faster than a regular CFD solver. Translation of interactive CFD simulation on local consumer computing hardware enables new applications in real-time predictions on the internet of things devices where data transfer is prohibitive and can increase the scale, speed, and computational cost of boundary-value fluid problems.