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Numerical Analysis Seminar
Seminar information archive ～09/24｜Next seminar｜Future seminars 09/25～
| Date, time & place | Tuesday 16:30 - 18:00 002Room #002 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Norikazu Saito, Takahito Kashiwabara |
Next seminar
2026/10/06
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Yohance Osborne (Durham University)
Numerical approximation of mean field games systems (English)
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Yohance Osborne (Durham University)
Numerical approximation of mean field games systems (English)
[ Abstract ]
Mean field games (MFG) are models for Nash equilibria of competitive differential games of optimal control involving a continuum of players. MFG equilibria are often described by systems of partial differential equations, where a Hamilton–Jacobi–Bellman (HJB) equation for the representative player’s value function is coupled nonlinearly with a Kolmogorov–Fokker–Planck (KFP) equation that determines the player distribution. MFG systems are particularly challenging to approximate computationally because they exhibit the following difficulties all at once: nonlinear couplings between the HJB and KFP equations, a temporal forward–backward structure, non-negativity of absolutely continuous player distributions, as well as potential nondifferentiability of the Hamiltonian. This talk addresses the numerical approximation of MFG systems for two classes of numerical schemes: (1) monotone stabilized finite element methods for second-order MFG systems with nondifferentiable Hamiltonians, and (2) particle methods for first-order MFG systems under displacement monotonicity. I will present theorems on the strong convergence of these numerical schemes and their rates of convergence, along with discussion of some numerical experiments.
[ Reference URL ]Mean field games (MFG) are models for Nash equilibria of competitive differential games of optimal control involving a continuum of players. MFG equilibria are often described by systems of partial differential equations, where a Hamilton–Jacobi–Bellman (HJB) equation for the representative player’s value function is coupled nonlinearly with a Kolmogorov–Fokker–Planck (KFP) equation that determines the player distribution. MFG systems are particularly challenging to approximate computationally because they exhibit the following difficulties all at once: nonlinear couplings between the HJB and KFP equations, a temporal forward–backward structure, non-negativity of absolutely continuous player distributions, as well as potential nondifferentiability of the Hamiltonian. This talk addresses the numerical approximation of MFG systems for two classes of numerical schemes: (1) monotone stabilized finite element methods for second-order MFG systems with nondifferentiable Hamiltonians, and (2) particle methods for first-order MFG systems under displacement monotonicity. I will present theorems on the strong convergence of these numerical schemes and their rates of convergence, along with discussion of some numerical experiments.
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
