# UCLA Math professors will lead a new Air Force Office of Scientific Research MURI project

UCLA Math Profs. Wilfrid Gangbo, Stanley Osher, and Wotao Yin will lead a new Air Force Office of Scientific Research MURI (multi-university research initiative) project on mean-field games. They will collaborate with UCLA CAM Assistant Profs. Yat-tin Chow and Wuchen Li, and with partners from U. Houston (Prof. Zhu Han), U. Maryland (Profs. Michele Gelfand, Tom Goldstein, and Dana Nau), and Princeton (Prof. H. Vincent Poor). Prof. Osher is the lead PI of this team.

The team will develop new and comprehensive mathematical approaches, with novel fast and parallelizable numerical algorithms, to study differential games for a large number of agents. This research will help develop and design systematic ways for modeling population genetics, human/animal behavior, ecology, the evolution of social cooperation, economics (trading), human/machine networks including transport networks, cyber networks and beyond.

Mean field games study dynamical strategic decision making in large populations of the individual players where each is affected only by specific averaged quantities of all the others. The mean-field refers to representing the behavior of a large number of agents by their population density function. This setting connects deeply with optimal transport theory, Nelson's stochastic mechanics (Schrodinger equation, Schrodinger bridge problem), partial differential equations, optimization, probability and statistics with applications in machine learning problems (reinforcement learning).

The multi-university team will receive $1.5 million per year in funding for three years with a two-year option.