Аннотация: 

The paper formulates and numerically studies the direct and inverse problems for the mean field game model, which describes the process of information dissemination in online social networks taking into account external influences. The mean field game model is reduced to a joint solution of initial-boundary value problems for the Kolmogorov-Fokker-Planck (KFP) and Hamilton-Jacobi-Bellman (HJB) equations, as well as the Nash optimality condition. ased on the Sobol global sensitivity analysis, the sensitivity of the function of measuring the user density at fixed times from the start of information dissemination to the control parameters and the initial condition of the KFP problem is shown. An algorithm for numerically solving inverse problems for the KFP and HJB equations that differ in the control function is constructed based on Bayesian optimization. It is shown that the reconstructed initial user density of the network describes the synthetic data of the inverse problem with greater accuracy in the case of fixed control, which is optimal for the exact solution of the inverse problem.