TY - GEN

T1 - Numerical Solution of the Inverse Problem for Diffusion-Logistic Model Arising in Online Social Networks

AU - Krivorotko, Olga

AU - Zvonareva, Tatiana

AU - Zyatkov, Nikolay

N1 - Publisher Copyright: © 2021, Springer Nature Switzerland AG.

PY - 2021

Y1 - 2021

N2 - The information propagation in online social networks is characterized by a nonlinear partial differential equation with the Neumann boundary conditions and initial condition (source) that depends on the type of information and social network. The problem of source identification using additional measurements of the number of influenced users with a discrete distance at fixed times is numerically investigated. One way to solve the source problem for the diffusive-logistic model is to reduce it to the minimization least squares problem that is solved by a combination of the global particle swarm optimization and the local Nelder-Mead methods. Another way is to construct the function of the density of influenced users in space and time that describes additional measurements with high accuracy using a machine learning method named artificial neural networks. The results of numerical calculations for synthetic data show the accuracy of 99% of the source reconstruction. The neural networks approximate additional measurements with lower accuracy, but the approximation function satisfies the diffusive-logistic mathematical model. The novelty lies in the comparative analysis of the stochastic method for minimizing the misfit function based on the structure of the model, and the machine learning approach, which does not use the mathematical model while learning.

AB - The information propagation in online social networks is characterized by a nonlinear partial differential equation with the Neumann boundary conditions and initial condition (source) that depends on the type of information and social network. The problem of source identification using additional measurements of the number of influenced users with a discrete distance at fixed times is numerically investigated. One way to solve the source problem for the diffusive-logistic model is to reduce it to the minimization least squares problem that is solved by a combination of the global particle swarm optimization and the local Nelder-Mead methods. Another way is to construct the function of the density of influenced users in space and time that describes additional measurements with high accuracy using a machine learning method named artificial neural networks. The results of numerical calculations for synthetic data show the accuracy of 99% of the source reconstruction. The neural networks approximate additional measurements with lower accuracy, but the approximation function satisfies the diffusive-logistic mathematical model. The novelty lies in the comparative analysis of the stochastic method for minimizing the misfit function based on the structure of the model, and the machine learning approach, which does not use the mathematical model while learning.

KW - Artificial neural networks

KW - Diffusion-logistic model

KW - Ill-posed problem

KW - Inverse problem

KW - Particle swarm optimization

KW - Regularization

KW - Singular value decomposition

KW - Social networks

KW - Source problem

KW - Stability analysis

UR - http://www.scopus.com/inward/record.url?scp=85115820760&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-86433-0_31

DO - 10.1007/978-3-030-86433-0_31

M3 - Conference contribution

AN - SCOPUS:85115820760

SN - 9783030864323

T3 - Communications in Computer and Information Science

SP - 444

EP - 459

BT - Mathematical Optimization Theory and Operations Research

A2 - Strekalovsky, Alexander

A2 - Kochetov, Yury

A2 - Gruzdeva, Tatiana

A2 - Orlov, Andrei

PB - Springer Science and Business Media Deutschland GmbH

T2 - 20th International Conference on Mathematical Optimization Theory and Operations Research , MOTOR 2021

Y2 - 5 July 2021 through 10 July 2021

ER -