Artificial Neural Networks in Fluid Dynamics: A Novel Approach to the Navier-Stokes Equations

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, Reynold's 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 67% accuracy of the validation data used. Further studies will focus on higher accuracy and solving further non-linear differential equations using convolutional neural networks.