[@wikle2002kernel; @cressie2011statistics]. A simple approach for spatiotemporal modeling is to utilize both spatial and temporal variables as inputs to the kernel [@perez:13:gaussian; @Chowdhary13_ACC2]. However, this technique leads to an ever-growing kernel dictionary, which is computationally taxing. Furthermore, constraining the dictionary size or utilizing a moving window will occlude the learning of long-term patterns. Periodic or nonstationary covariance functions and nonlinear transformations have been proposed to address this issue [@ma2003nonstationary; @RasmussenWilliams2005]. Furthermore, work in the design of nonseparable and nonstationary covariance kernels seeks to design kernels optimized to environment-specific dynamics, and optimize their hyperparameters in local regions of the input space [@garg2012AAAI; @das2014nonstationary; @plagemann2008nonstationary]. The model of spatiotemporal functional evolution proposed in this paper builds on the idea that modeling the temporal evolution of mixing weights of a kernel model is a valid approach to spatiotemporal modeling. The key idea behind our approach is that the spatiotemporal evolution of a kernel-based model can be directly modeled by tracing the evolution of the mean embedded in a RKHS using switched ordinary differential equations (ODE) when the evolution is continuous, or switched difference equations when it is discrete (Figure \[fig:hilbert\_evolution\]). The advantage of this approach is that it allows us to utilize powerful 