Stacked Generative Machine Learning Models for Fast Approximations of Steady-State Navier-Stokes Equations
This enables real-time fluid dynamics predictions on consumer hardware, such as IoT devices, by reducing computational costs and data transfer needs, though it is incremental as it builds on existing machine learning methods for CFD.
The paper tackles the computational inefficiency of solving steady-state Navier-Stokes equations in fluid dynamics by developing a stacked generative machine learning model that uses a weakly-supervised, physics-informed approach without labeled simulation data, achieving results 1000 times faster than traditional CFD solvers on a 64 x 64 domain.
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.