流体动力学中的人工神经网络：求解纳维-斯托克斯方程的新方法
Artificial Neural Networks in Fluid Dynamics: A Novel Approach to the Navier-Stokes Equations
AI总结：
本文提出利用神经网络结合贝叶斯聚类和SOM邻域加权方法，基于三维输入数据映射电离层速度场，验证了神经网络在求解湍流纳维-斯托克斯方程中的有效性。
摘要：
神经网络已被用于解决许多不同领域中的大规模数据相关问题。本项目采用新颖的方法，通过训练神经网络来求解湍流的纳维-斯托克斯方程，利用贝叶斯聚类和SOM邻域加权方法，基于三维输入数据映射电离层速度场。该问题中使用的参数包括速度、雷诺数、普朗特数和温度。本项目使用马歇尔大学的数据在MATLAB中训练神经网络。神经网络能够以67%的准确度映射验证数据中的速度场。进一步的研究将专注于提高精度并使用卷积神经网络求解更多的非线性微分方程。
英文摘要：
Neural networks have been used to solve different types of large data related problems in many different fields.This project takes a novel approach to solving the Navier-Stokes Equations for turbulence by training a neural network using Bayesian Cluster and SOM neighbor weighting to map ionospheric velocity fields based on 3-dimensional inputs. Parameters used in this problem included the velocity, Reynolds number, Prandtl number, and temperature. In this project data was obtained from Johns-Hopkins University to train the neural network using MATLAB. The neural network was able to map the velocity fields within a sixty-seven percent accuracy of the validation data used. Further studies will focus on higher accuracy and solving further non-linear differential equations using convolutional neural networks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
