Convexification for a Coefficient Inverse Problem for a System of Two Coupled Nonlinear Parabolic Equations

TL;DR

This paper develops a numerical method with proven convergence for solving coefficient inverse problems in a mean field games system, a class of coupled nonlinear parabolic PDEs with applications in social sciences.

Contribution

It introduces a novel convexification approach for the CIP in MFG systems, with theoretical convergence guarantees and numerical validation.

Findings

The method converges globally for the considered inverse problem.

Numerical experiments demonstrate the effectiveness of the approach.

The approach advances computational techniques in MFG coefficient inverse problems.

Abstract

A system of two coupled nonlinear parabolic partial differential equations with two opposite directions of time is considered. In fact, this is the so-called "Mean Field Games System" (MFGS), which is derived in the mean field games (MFG) theory. This theory has numerous applications in social sciences. The topic of Coefficient Inverse Problems (CIPs) in the MFG theory is in its infant age, both in theory and computations. A numerical method for this CIP is developed. Convergence analysis ensures the global convergence of this method. Numerical experiments are presented.