Behavior of Solutions of Model-Free Prediction of the Differential Equation describing the Phenomenon using RNN

Abstract

Various phenomena in the real world can be described using mathematical models, e.g., differential equations, and be revealed by solving these equations. We then predict behavior of the corresponding phenomena. However, in general, it is difficult to solve differential equations by using mathematical analysis. Also, there are methods using numerical computations, but it is difficult due to complex structure of equations and the initial value sensitivity, etc. To overcome this problem, the reservoir computing, which is one of machine learning algorithms, has been proposed for predicting the solution of the Kuramoto-Shivashinsky equation. In this thesis, we propose deep recurrent neural network for predicting the solutions of differential equations in order to find more suitable algorithm than the reservoir computing in the preceding work. In addition, we show the prediction result of behavior of solution of the differential equation using Deep Recurrent Neural Network.