Kernel Observers: Systems-Theoretic Modeling and Inference of Spatiotemporally Varying Processes

We consider the problem of estimating the latent state of a spatiotemporally evolving continuous function using very few sensor measurements. We show that a dynamical systems layer over temporal evolution of the weights of a kernel model is a valid approach to spatiotemporal modeling that does not necessarily require the design of complex nonstationary kernels. Furthermore, we show that such a predictive model can be utilized to determine sensing locations that guarantee that the hidden state of the predictive model can be recovered with very few measurements. The approach is validated on real-world datasets.