  We formulate a data-driven method for constructing finite volume
discretizations of a dynamical system's underlying Continuity / Fokker-Planck
equation. A method is employed that allows for flexibility in partitioning
state space, generalizes to function spaces, applies to arbitrarily long
sequences of time-series data, is robust to noise, and quantifies uncertainty
with respect to finite sample effects. After applying the method, one is left
with Markov states (cell centers) and a random matrix approximation to the
generator. When used in tandem, they emulate the statistics of the underlying
system. We apply the method to the Lorenz equations (a three-dimensional
ordinary differential equation) and a modified Held-Suarez atmospheric
simulation (a Flux-Differencing Discontinuous Galerkin discretization of the
compressible Euler equations with gravity and rotation on a thin spherical
shell). We show that a coarse discretization captures many essential
statistical properties of the system, such as steady state moments, time
autocorrelations, and residency times for subsets of state space.
