Analysis of accuracy and efficiency of neural networks to simulate Navier-Stokes fluid flows with obstacles

TL;DR

This paper demonstrates that neural networks can accurately and efficiently simulate incompressible fluid flows around obstacles, offering a faster alternative to traditional numerical methods with acceptable error margins for short-term predictions.

Contribution

The study introduces a neural network approach for simulating obstacle-heavy fluid flows, achieving low error rates and significantly faster predictions compared to conventional simulations.

Findings

Root mean square error of 0.36% on test data

Neural network predictions are approximately 8,800 times faster

Errors grow but remain manageable over multiple time steps

Abstract

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 obstacle-heavy 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 t = 10 and, 2.11% and 4.16% at timestep t = 20. We also found that our selected neural network was approximately 8,800 times faster at predicting the flow than a conventional simulation. Our findings indicate 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.