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 u<inf>t</inf> = (D(x)u<inf>x</inf>)<inf>x</inf> +ν(C(x)u(x))<inf>x</inf> + f (xt) using Neumann type boundary measurements. The nonlocal condition enables us to reduce the parabolic 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 Optimization. The efficiency and applicability of the method is demonstrated using various numerical examples with noisy free and noisy data. © 2022 Elsevier B.V. All rights reserved.