Accepted_test

Mathematical models of the dynamics of social processes are poorly understood and rely on systems of differential equations and agent-based models. Due to incomplete data, the use of these models does not fully characterize the process and its control. It is necessary to use the mean-field methodology based on the dual game that allows one optimal control the information dissemination in online social networks.
We consider a large number of users who can take states x∈[0,1], where 0 means that the user is involved in the information dissemination process and 1 means the opposite. Then the density of users u(x,t) satisfies the Kolmogorov (Fokker-Planck) equation. Here, α(x,t) is the control parameter (in other words, the user strategy) that ensures the Nash equilibrium of the system of interacting agents and minimizes the cost functional J with respect to (u,α).
Using the Lagrange multiplier method, a system similar to the Hamilton-Jacobi-Bellman equation is constructed.
The identifiability of the model was analyzed by the Sobol sensitivity analysis method.
For the case α=0 (without control) we minimized the target functional using:
- the tensor optimization method (TT),
- the combination of TT and fast gradient method (FGM),
- the combined method with A.N. Tikhonov regularization,
- the combination of stochastic particle swarm optimization (PSO) and FGM.
The study is supported by the Russian Science Foundation (pro-ject No. 23-71-10068).