Neural Network Solver for Transient State Incompressible Flow on Arbitrarily-Shaped Geometries Defined using Bezier Curves

Models that can simulate turbulent fluid flow have numerous industrial applications. Indeed, fluid modeling is a key component of the design process for everything from airplanes to soccer balls. Current methods for modeling turbulent fluids are accurate but slow. As a result, much research has been published on neural networks that can predict fluid flow with inference times that are orders of magnitude faster than traditional methods such as Large Eddy Simulation, Direct Numerical Simulation, and Reynolds Averaged Navier Stokes. To enable the neural network to predict the fluid flow around any arbitrarily-shaped obstruction, the prevailing technique is to input the simulation grid into the neural network in the form of a point cloud or image. In this research, we propose a simpler approach. Instead of a point cloud, we define the boundary of an arbitrary obstruction using a handful of points. All intermediate points will then be interpolated using Bezier curves. Using fewer points allows for improved training time, inference time, and neural network size. Our research created two physics informed neural networks, each a few hundred kilobytes, that can predict transient-state turbulent fluid flow with a mean squared error of 1.866E-05, with the error continuing to drop with further training. The training time was as low as 38.50 hours on a CPU. The inference time was only 3 seconds. Our proposed technique will have even more benefit when modeling fluid flow over 3D topographic maps, which are ideally suited for interpolation using curves.