Numerical methods of artificial neural network training

The problem of artificial neural network modeling is studied. The artificial neural network is characterized by the enough general topology and is described by the system of integral differential equations. Training on the artificial neural network usage is considered as an optimal control problem with variable duration of the process. Considering the defined constraints and the form of the functional, the necessary conditions of optimality of the artificial neural network weighting coefficients incorporating external influence are formulated. The initial current problem is reduced to a discrete optimal control problem, which is solved by the methodology of the fast automatic differentiation. The influence of the task parameters on the optimal solution is analyzed.