SFU Mathematics of Computation, Application and Data ("MOCAD") Seminar: Siting Liu

Mean-field game (MFG) systems provide a powerful framework for modeling the collective behavior of multi-agent systems with diverse applications. However, unknown parameters pose challenges. In this work, we tackle an inverse problem, recovering MFG parameters from limited, noisy boundary observations. Despite the problem's ill-posed nature, we aim to efficiently retrieve these parameters to understand population dynamics. Our focus is on recovering running cost and interaction energy in MFG equations from boundary measurements. We formalize the problem as a constrained optimization problem with L1 regularization. We then develop a fast and robust operator splitting algorithm to solve the optimization using techniques, including harmonic extensions, a three-operator splitting scheme, and the primal-dual hybrid gradient method. Numerical experiments illustrate the effectiveness and robustness of the algorithm. This is joint work with Yat Tin Chow (UCR), Samy Wu Fung (Colorado School of Mines), Levon Nurbekyan (Emory), and Stanley J. Osher (UCLA).