An Investigation into a Neural Network's performance based on the Number of Neurons in the Hidden Layer

Abstract

An important benchmark for closed-loop flow control is the suppression of the von Karman vortex street in the wake of a circular cylinder at a Reynolds number of 100. A low-dimensional Proper Orthogonal Decomposition (POD) is applied to the flow field and a four sensor configuration is placed based on the intensity of the resulting spatial Eigenfunctions. This effort focuses on the performance of a non-linear Artificial Neural Network Estimator (ANNE) used for real-time mapping of flow field sensors to POD states. This investigation examines the sensitivity of ANNE by varying the number of neurons in the hidden layer. The aim is to determine if there is an optimum number of neurons in the hidden layer. Three input data sets were studied, the first had no noise on the training and testing data, the second had 10% noise applied to the training and testing data, and the third had 25% noise applied to the training and testing data sets. In all cases 50 randomly selected training data sets were applied to the back-propagating network. A separate data set was used for testing the feed-forward network. During the validation process, network outputs were compared to desired outputs and the Root Mean Squared (RMS) error was calculated for each of the four output nodes. Results show that in general, the more nodes in the hidden layer the better the performance of the network. However, there appeared to be a consistently reduced error when eight (8) nodes were used in the hidden layer. Results from ANNE when compared to the state-of-the-art Linear Stochastic Estimator (LSE) shows significant benefits.