Solving initial value problems using artificial neural networks

In this paper, a method based on feed-forward neural network with appropriate activation functions is proposed to solve initial value problems. The proposed method, like spectral methods, approximates the solution value at any arbitrary point in given interval. The proposed network has three layers. The input layer and the output layer have only one neuron, but the hidden layer has an arbitrary number of neurons. The activation functions can be changed according to the given problem. To train the network, we select a number of points from the given interval as co-local points. The provided examples show that the number of neurons in the hidden layer as well as the number of collocation points considered are effective in the accuracy of the proposed method.

Keywords:

Feedforward neural networks , Initial value problems , Spectral method , Collocation method