Model Free Prediction Using RNN for Behavior of the solution of Duffing Equation

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  • RNN による Duffing 方程式の解のふるまいのモデルフリー予測
  • RNN ニ ヨル Duffing ホウテイシキ ノ カイ ノ フルマイ ノ モデルフリー ヨソク

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Abstract

<p>Differential equations are used in order to understand natural or social phenomena. If one solves the differential equations, behavior of the solution reveals the phenomena more efficiently. However, some of differential equations are difficult to solve in the way of mathematical analysis. Recently, for this problem, the model free prediction can be used to figure out the behavior of the solution. For example, there is a preceding study of the model free prediction for the spatiotemporal chaotic behavior of the solution of the Kuramoto-Sivashinsky equation by using the reservoir computing, which is one of the machine learning scheme. The reservoir computing is a type of the recurrent neural network, whose feature is that one only trains the output weight. On the other hand, this paper proposes a scheme of customized recurrent neural network that trains all weights. In order to show how the proposed scheme works, we apply the scheme to predicting behavior of solutions to the Duffing equation, which is a nonlinear model for dumped and driven oscillators.</p>

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