用神经网络模拟有障碍物的流体，速度快且误差可控。
Analysis of accuracy and efficiency of neural networks to simulate Navier-Stokes fluid flows with obstacles
- 用神经网络直接预测流体在障碍物环境中的演化，跳过传统方程求解。
- 20步后误差仅4.16%，但速度比传统方法快8800倍。
- 适合需要快速仿真流体的场景，如火灾烟雾、管道流动。
传统流体模拟耗时且能耗高。本文研究了神经网络在随机障碍物密集环境中的不可压缩流体模拟可行性，作为纳维-斯托克斯方程数值求解的替代方案。假设神经网络在短时间步内误差较小，但随时间推移误差会累积。在大量障碍物配置下，训练集上均方根误差为0.32%，测试集为0.36%。在t=10时误差增长至1.45%和2.34%，t=20时分别达2.11%和4.16%。所选神经网络预测速度约为传统模拟的8800倍。结果表明，神经网络可在障碍物密集环境中高效模拟流体，适用于森林火灾烟雾、管道流体及水下/洪水流等场景。
原文摘要 · Abstract (English)
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.
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