UC Santa Barbara

We discretize spatial domains into lattices. We provide the multivariate Fokker-Planck partial differential equation and its numerical solutions. We establish our convolutional neural network details, aiming to train these networks on our Fokker-Planck data with the goal of recovering Fokker-Planck coefficients. We break up our objective into different cases. For each case, we discuss results. First, we consider the simplified diffusion equation, then the advection-diffusion equation, where our networks learn the differential operators. We consider long-time integration methods. Finally, we consider finite difference and finite volume methods.