Comparison of two neural network approaches to modeling processes in a chemical reactor

Abstract

In this paper, we conduct the comparative analysis of two neural network approaches to the problem of constructing approximate neural network solutions of non-linear differential equations. The first approach is connected with building a neural network with one hidden layer by minimization of an error functional with regeneration of test points. The second approach is based on a new continuous analog of the shooting method. In the first step of the second method, we apply our modification of the corrected Euler method, and in the second and subsequent steps, we apply our modification of the St?rmer method. We have tested our methods on a boundary value problem for an ODE which describes the processes in the chemical reactor. These methods allowed us to obtain simple formulas for the approximate solution of the problem, but the problem is special because it is highly non-linear and also has ambiguous solutions and vanishing solutions if we change the parameter value.