CONVEXIFICATION NUMERICAL METHOD FOR A COEFFICIENT INVERSE PROBLEM FOR THE SYSTEM OF NONLINEAR PARABOLIC EQUATIONS GOVERNING MEAN FIELD GAMES

The Mean Field Games theory has applications in mathematical modeling of various social phenomena. The key to this theory is the Mean Field Games System (MFGS) of two coupled nonlinear parabolic Partial Differential Equations with two opposite directions of time. One of those equations contains an integral operator, the so-called global interaction term. The topic of Coefficient Inverse Problems (CIPs) for the MFGS is in its infant age. In this paper, a CIP for the MFGS is solved numerically by a globally convergent convexification method. A coefficient characterizing the global interaction term is recovered from the single measurement data. A detailed global convergence analysis, based on Carleman estimates, is presented. Numerical results demonstrate accurate reconstructions from noisy data.