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

• Published in: Computational mathematics and mathematical physics Vol. 63; no. 9; pp. 1654 - 1663
• Main Authors: Zvonareva, T. A., Kabanikhin, S. I., Krivorotko, O. I.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.09.2023; Springer Nature B.V
• Subjects: Algorithms; Artificial intelligence; Boundary value problems; Computational Mathematics and Numerical Analysis; Flow velocity; Information dissemination; Inverse problems; Mathematical analysis; Mathematics; Mathematics and Statistics; Numerical analysis; Operators (mathematics); Optimal Control; Optimization; Regularization; Social networks; Tensors; inverse problem; tensor optimization; reaction–diffusion model; source determination problem; gradient methods; regularization
• ISSN: 0965-5425; 1555-6662
• DOI: 10.1134/S0965542523090166

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.