A deep learning approximation of non-stationary solutions to wave kinetic equations

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