COMPARISON OF CLASSICAL METHODS FOR NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS WITH THE NEURAL NETWORK METHOD

Akhmetov Ilshat Zufarovich

In this paper, the method of artificial neural networks was constructed for the numerical solution of various differential equations types. This method is also known as the PINN, i.e. physics-informed neural network. The main idea of the method is to minimize the squared residual of the equation, in which the solution of the equation is sought using an artificial neural network. Currently there are many researches related to this method, thus there is need to examine this method in detail and compare with other methods, first of all the classical ones. A number of examples was provided in order to compare this method with classical methods for the numerical solution of differential equations in terms of accuracy. In order to implement the neural network method author developed a program on python programming language using PyTorch - a framework for deep learning.

Keywords:artificial neural networks, differential equations, approximation, numerical methods