  We present a deep learning approximation, stochastic optimization based,
method for wave kinetic equations. To build confidence in our approach, we
apply the method to a Smoluchowski coagulation equation with multiplicative
kernel for which an analytic solution exists. Our deep learning approach is
then used to approximate the non-stationary solution to a 3-wave kinetic
equation corresponding to acoustic wave systems. To validate the neural network
approximation, we compare the decay rate of the total energy with previously
obtained theoretical results. A finite volume solution is presented and
compared with the present method.
