Applied Math Seminar-An Inverse Problem in Mean Field Games from Partial Boundary Measurement

Time: Friday, Nov. 18th. 3:30-4:30 pm

Place: Zoom

Zoom link: https://gwu-edu.zoom.us/j/95630895609

Speaker: Siting Liu, UCLA

Title: An Inverse Problem in Mean Field Games from Partial Boundary Measurement

Abstract: In this talk, we consider a novel inverse problem in mean-field games (MFG). We aim to recover the MFG model parameters that govern the underlying interactions among the population based on a limited set of noisy partial observations of the population dynamics under the limited aperture. Due to its severe ill-posedness, obtaining a good quality reconstruction is very difficult. Nonetheless, it is vital to recovering the model parameters stably and efficiently to uncover the underlying causes of population dynamics for practical needs.

Our work focuses on the simultaneous recovery of running cost and interaction energy in the MFG equations from a finite number of boundary measurements of population profile and boundary movement. To achieve this goal, we formalize the inverse problem as a constrained optimization problem of a least squares residual functional under suitable norms. We then develop a fast and robust operator splitting algorithm to solve the optimization using techniques including harmonic extensions, three-operator splitting scheme, and primal-dual hybrid gradient method. Numerical experiments illustrate the effectiveness and robustness of the algorithm.
This is a joint work with Yat Tin Chow, Samy Wu Fung, Levon Nurbekyan and Stanley J. Osher.