a mean field game is usually denoted as a game with the number of players tending to infinity, which leads us to consider population densities of players and their resulting ``nash equilibrium'' strategies. mean field games have been used to model financial markets, population dynamics, and more, but solving the mean field games ends up requiring us to solve a high-dimensional pde. to avoid the curse of dimensionality, we can instead use the method of characteristics to turn one of the pdes in the mean field game into a system of odes and then solve the mean field game by parameterizing the dynamics of the ode with a neural network.