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

arXiv: https://arxiv.org/abs/2510.22976 · HTML: https://mlsanity.com/paper/2510.22976/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 5 references that are in the map.
- First posted on arXiv 27 Oct 2025.

## Builds on (most cited first, 2 of 2)

- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [A Pioneering Neural Network Method for Efficient and Robust Fluid Simulation](https://mlsanity.com/paper/2412.10748/) (2024)

## Abstract (arXiv)

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.