# An exact kernel framework for spatio-temporal dynamics

@article{Szehr2020AnEK, title={An exact kernel framework for spatio-temporal dynamics}, author={Oleg Szehr and Dario Azzimonti and Laura Azzimonti}, journal={arXiv: Statistics Theory}, year={2020} }

A kernel-based framework for spatio-temporal data analysis is introduced that applies in situations when the underlying system dynamics are governed by a dynamic equation. The key ingredient is a representer theorem that involves time-dependent kernels. Such kernels occur commonly in the expansion of solutions of partial differential equations. The representer theorem is applied to find among all solutions of a dynamic equation the one that minimizes the error with given spatio-temporal samples…

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