  The celebrated Krusel-Smith growth model is an important example of a Mean
Field Game with a common noise. The Mean Field Game is encoded in the master
equation, a partial differential equation satisfied by the value of the game
which depends on the whole distribution of states. The latter equation is
therefore posed in an infinite dimensional space. This makes the numerical
simulations quite challenging. However, Krusell and Smith conjectured that the
value function of the game mostly depends on the state distribution through low
dimensional quantities. In this paper, we wish to propose a numerical method
for approximating the solutions of the master equation arising in Krusell-Smith
model, and for adaptively identifying low-dimensional variables which retain an
important part of the information. This new numerical framework is based on a
semi-Lagrangian method and uses neural networks as an important ingredient.
