Tensor train optimization for mathematical model of social networks

TL;DR

This paper introduces a tensor train decomposition-based optimization method for solving inverse problems in social network models, combining global convergence with local gradient techniques for improved accuracy.

Contribution

The paper presents a novel tensor train optimization approach for inverse problems in social network models, integrating global and local methods for enhanced solution accuracy.

Findings

Tensor train decomposition effectively captures the structure of the optimization functional.

The combined approach improves convergence and solution quality for social network inverse problems.

Numerical results demonstrate the method's applicability to real-world social network models.

Abstract

The optimization algorithms for solving multi-parameter inverse problem for the mathematical model of parabolic equations arising in social networks, epidemiology and economy are investigated. The data fitting is formulated as optimization of least squares misfit function. Firstly, the tensor train decomposition approach is presented as global convergence algorithm. The idea of proposed method is to extract the tensor structure of the optimized functional and use it for optimization. Then the inverse problem solution is reached by implementation of the local gradient approach. The evident formula for the gradient of the misfit function is obtained. The inverse problem for the diffusive logistic mathematical model described online social networks is solved by combination of tensor train optimization and local gradient methods. The numerical results are presented and discussed.