include active wing-shaping based control of flexible aircraft, control of heat or particulate diffusion in manufacturing processes, control of rumor spreading across a social network, and tactical asset allocation and control problems in dynamically varying battlespaces. The traditional approach to modeling and control of spatiotemporal systems have relied on Partial Differential Equations (PDEs) [@Alabau2012controlpde], solutions to which are functions that evolve in both space and time. However, PDE models can be limited in situations where exact physics based models of the functional evolution are difficult to formulate, or are inherently limited due to the physical understanding of the process or unknown spatiotemporal interactions [@cressie2011statistics]. Furthermore, the control of PDEs is fundamentally more challenging than the control of finite-dimensional state-space systems because the evolution and control spaces are infinite dimensional Hilbert spaces, as opposed to $\mathbb{R}^n$ [@Alabau2012controlpde].

Accordingly, there has been significant work in approximate modeling of spatiotemporally evolving functions using data-driven or distributed parameter based approximations of PDEs [@cressie2011statistics; @wikle2001kernel]. One way to model spatiotemporally evolving functions is to approximate the function at several sampling locations and build an autoregressive model of the evolution of the function’s output over that grid [@baker2000finite]. The fidelity of these models heavily depends on 