kernel. The set of atoms ${\mathcal{F}_{{C}}}$ was determined through a linear independence test based sparsification algorithm [@csato2002sparse]. Once the parameters were chosen, a budgeted GP was learned for each date, resulting in weight vectors ${w}_i, \ i\in\{1,2,\dots,365\}$. We used Algorithm \[alg:egp\_trans\] to infer ${\widehat{A}}$, and applied Algorithm \[alg:egp\_inf\] with ${N}\in \{280,500,1000,2000\}$ chosen randomly in the ${\Omega}$ to track the system state given a random initial condition ${w}_0$. Figures \[fig:pathfinder\_errors\_boxplots\_day\] and \[fig:pathfinder\_errors\_boxplots\] show a comparison of the deviation in percentage of the estimated values from the real data, averaged over all the days. As can be seen, the observer enables the prediction of functional evolution *without needing all the measurements (37 million)*, and performance comparable to sampling over all locations is obtained with sampling only over $2,000$ locations. Note that here, even though the system model is observable at ${N}=280$, since the dynamics are not truly linear in ${\ensuremath{{\mathcal{H}}_{{C}}}}$, we get better performance with more sampling locations. Finally, \[fig:pathfinder\_tr\_times\_boxplots\_day\] and \[fig:pathfinder\_tr\_times\_boxplots\] show that the time required to estimate the state during function tracking with kernel observer are an order of magnitude better than retraining the model every time step (“original” in the figure), with comparable performance.

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Control of a linear 