Simultaneously decoding the unknown stationary state and function parameters for mean field games

TL;DR

This paper introduces a novel unified method to simultaneously decode the unknown stationary state and parameters of mean field games, significantly advancing inverse problem solutions for nonlinear PDEs and enhancing practical applications.

Contribution

It develops a new approach to recover both the stationary state and underlying functions in MFGs, a problem previously unaddressed in nonlinear PDE inverse problems.

Findings

Successfully decodes unknown stationary states from data

Identifies underlying parameter functions governing MFGs

Enhances the practical deployment of MFG models

Abstract

Mean field games (MFGs) offer a versatile framework for modeling large-scale interactive systems across multiple domains. This paper builds upon a previous work, by developing a state-of-the-art unified approach to decode or design the unknown stationary state of MFGs, in addition to the underlying parameter functions governing their behavior. This result is novel, even in the general realm of inverse problems for nonlinear PDEs. By enabling agents to distill crucial insights from observed data and unveil intricate hidden structures and unknown states within MFG systems, our approach surmounts a significant obstacle, enhancing the applicability of MFGs in real-world scenarios. This advancement not only enriches our understanding of MFG dynamics but also broadens the scope for their practical deployment in various contexts.