Analysis of the Accuracy and Efficiency of Neural Networks to Simulate Navier-Stokes Fluid Flows with Obstacles

Conventional fluid simulations can be time consuming and energy intensive. We researched the viability of a neural network for simulating incompressible fluids in a randomized obstacleheavy environment, as an alternative to the numerical simulation of the Navier-Stokes equation. We hypothesized that the neural network predictions would have a relatively low error for simulations over a small number of time steps, but errors would eventually accumulate to the point that the output would become very noisy. Over a rich set of obstacle configurations, we achieved a root-mean-square-error of 0.32% on our training dataset and 0.36% on a testing dataset. These errors only grew to 1.45% and 2.34% at time step t = 10 a nd, 2 .11% a nd 4 .16% a t t ime s tep t = 2 0. We a lso f ound t hat a n a ccurate neural network can be approximately 8,800 times faster at predicting the flow than a conventional simulation. These findings indicate that neural networks can be extremely useful at simulating fluids in obstacle-heavy environments. Useful applications include modeling forest fire smoke, pipe fluid flow, and underwater/flood currents.