Seminar: Forecasting in Mean Field Games via Convexification

Thời gian: 15:30 đến 17:00 Ngày 22/05/2025

Địa điểm: Phòng C101, VIASM, 157 phố Chùa Láng, Hà Nội

Báo cáo viên: Dr. Trương Thành Trung (Marshall University, USA)

Tóm tắt: Mean Field Games (MFGs) provide a powerful framework for modeling complex real-world phenomena, including the evolution of public sentiment. The MFG system consists of two coupled partial differential equations (PDEs) governing two key unknowns: the density of individuals holding a particular opinion and their expected reward associated with that opinion. A fundamental challenge in MFGs is the forecasting problem—predicting the evolution of both density and reward functions given their initial conditions. Due to the inherent instability of solutions, this problem remains notoriously difficult. Existing literature lacks a numerical method equipped with a rigorous convergence analysis for tackling this issue. Convexification, using Carleman estimates as its principal tool, has proven effective in addressing a broad range of forward and inverse problems in PDEs. Recently, two new Carleman estimates have been established, enabling the application of Convexification to the MFG forecasting problem. This talk will present both the theoretical foundation and numerical validation of this method. This is joint work with S. Chen, M. Klibanov, and K. McGoff.