Feedforward neural network with Reformulated Levenberg-Marquardt optimization algorithm for solving ordinary differential equations

• 1、College of Science, Inner Mongolia University of Technology, Hohhot 010051
• 2、Water Conservancy and Civil Engineering College, Inner Mongolia Agricultural University, Hohhot 010018

Abstract：This paper reformulates Levenberg-Marquardt (RLM) training algorithm in neural networks for solving ordinary differential equations (ODEs), and multiple joint training LM (MJLM) algorithm is proposed for solving coupled ODEs. However, there are several new approaches in literature to solve ODEs, but the new approach has more advantages, such as fast convergence and also little error. The optimal values for the corresponding adjustable parameters are calculated, an accurate approximate solution is obtained, which works well for interior and exterior points of the original domain. We show how to apply this method to a specific example of ODEs, the accuracy of the method is illustrated by solving several problems.

keywords： Reformulated LM training algorithm Multiple joint training LM algorithm ordinarydifferential equations

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