Numerical Algorithm for Source Determination in a Diffusion–Logistic Model from Integral Data Based on Tensor Optimization

Abstract

An algorithm has been developed for numerically solving the source determination problem in the model of information dissemination in synthetic online social networks, described by reaction–diffusion-type equations, using additional information about the process at fixed time points. The degree of ill-posedness of the source determination problem for a parabolic equation is studied based on the analysis of singular values of the linearized operator of the inverse problem. The algorithm developed is based on a combination of the tensor optimization method and gradient descent supplemented with the A.N. Tikhonov regularization. Numerical calculations demonstrate the smallest relative error in the reconstructed source obtained by the developed algorithm in comparison with classical approaches.