Application of artificial neural networks to solution of variational problems in hydrodynamics

Abstract

Abstract The paper deals with a combined approach to approximation of velocity fields and minimization the objective functional in solving viscous fluids flow problems. The mathematical formulation of the problem is presented in the form of a generalized Lagrange functional. The flow function is designed using a feed forward artificial neural network with one hidden layer and with logistic activation function. The boundary values of the flow function are determined using the fluid flow rate. Thus, the problem of determination the velocity field is reduced to the problem of finding the network weights by minimizing the generalized Lagrange functional.