ON A SOLUTION TO A NONLOCAL INVERSE COEFFICIENT PROBLEM USING FEED-FORWARD NEURAL NETWORKS

Abstract

This study gives a determination of the diffusion coefficient D(x) from the equation ut = (D(x)u(x))(x) + nu (C(x)u(x))(x) + f (xt) using Neumann type boundary measurements. The nonlocal condition enables us to reduce the par-abolic problem to a boundary-value problem for ODE. The flux data can be used for the initial condition of the Cauchy problem obtained from the reduced problem. The feed-forward neural network is used to find the solution to the corresponding inverse problem for D(x). The presented approach is based on the solution of a nonlinear optimization problem using Particle Swarm Opti-mization. The efficiency and applicability of the method is demonstrated using various numerical examples with noisy free and noisy data.