Refet Polat2025-10-06202224094986, 240949942409-49862409-499410.30546/2409-4994.48.2.2022.249https://www.scopus.com/inward/record.uri?eid=2-s2.0-85142604905&doi=10.30546%2F2409-4994.48.2.2022.249&partnerID=40&md5=9aafdeb1b69bf27d19b9a988ad087198https://gcris.yasar.edu.tr/handle/123456789/8782This 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.EnglishInverse Coefficient Problem, Neural Networks, Particle Swarm Optimization, Sludge ConcentrationArticle