Solving nonlinear Lane-Emden type equations with unsupervised combined artificial neural networks

In this paper we propose a method for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-innite domain. The proposed approach is based on an Unsupervised Combined Articial Neural Networks (UCANN) method. Firstly, The trial solutions of the differential equations are written in the form of feed-forward neural networks containing adjustable parameters (the weights and biases); results are then optimized with the combined neural network. The proposed method is tested on series of Lane-Emden differential equations and the results are reported. Afterward, these results are compared with the solution of other methods demonstrating the eciency and applicability of the proposed method.

Keywords:

Lane-Emden type equations , Nonlinear ODE , Semi-infinite domain , Astrophysics , Artificial neural network , Combined neural network