  Modeling geophysical systems as dynamical systems and regressing their vector
field from data is a simple way to learn emulators for such systems. We show
that when the kernel of these emulators is also learned from data (using kernel
flows, a variant of cross-validation), then the resulting data-driven models
are not only faster than equation-based models but are easier to train than
neural networks such as the long short-term memory neural network. In addition,
they are also more accurate and predictive than the latter. When trained on
observational data for the global sea-surface temperature, considerable gains
are observed by the proposed technique in comparison to classical partial
differential equation-based models in terms of forecast computational cost and
accuracy. When trained on publicly available re-analysis data for temperatures
in the North-American continent, we see significant improvements over
climatology and persistence based forecast techniques.
