Neural networking on function prediction

Abstract

Deep learning, the technique for performing neural network is a widely used tool for generalizing experimental result and further makes prediction on unknowns from existing results with a high accuracy. Nowadays, neural network and deep learning have become one of the most popular leading vogue in researches. It is widely applied for generalizing a huge amount of data, simulating real life situations or forecasting future tendency in different academic fields. This tool appearing in companies have rapidly grow due to its efficiency and convenient. In physics, many phenomena are governed by equations, with a known function type. However, since all measurement contains error and uncertainty, the equation may not be appeared very obviously within the result for a large database and hard to be accurately modeled, thus using neural network can highly increase the performance of equation predicted for the acquired result. Furthermore, after generalization of the training data, the network can be used to accurately predicts new data points beyond the given training data, which enable a broader hypothesis to be made for the experiment topic. Comparing with other algorithms for predicting the structure of a set of data, neural network gives an advantage of using layers of learning to perform approximation, instead of taking statistical assumption. This allows the situation to be more complex and real life. The reason behind these skillfully performed generalization and prediction on mystery data is that the training data are explicitly fitted into a function. Thus one of the most primary and important application of neural network is function prediction, which is focused strongly throughout this project. Throughout performing the neural network on various situations, accuracy for running the networking is find to be on average 94% for handwriting recognition and 96% for function prediction. Numerous parameters are adjusted while performing neural network such as learning rate and amount of training data always alters the performance of the outputting value. Although most of these parameters have a corresponding relationship with the performance, both extremely lowering or increasing these factors will also negatively affect the outcome. Thus finding the finest value for all parameters beneficial for neural network to perform with its top competency is the goal of this project. The application of neural network is also a main focus in this project, through generating new database for the training and testing data, along with modification of the original neural network code by Michael A. Nielsen (2015). Throughout this project, various functions including the cosine function and the exponential function are successfully approximated or predicted, in a satisfactory processing time and accuracy.