An exact kernel framework for spatio-temporal dynamics

• URL: http://arxiv.org/abs/2011.06848v1
• Date: Fri, 13 Nov 2020 10:32:34 GMT
• Title: An exact kernel framework for spatio-temporal dynamics
• Authors: Oleg Szehr, Dario Azzimonti, Laura Azzimonti
• Abstract summary: A kernel-based framework for system dynamics analysis is introduced. It applies to situations when the underlying system dynamics are governed by a dynamic equation.
• Score: 0.04297070083645048
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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. This is motivated by the fact that very often a differential equation is given a priori (e.g.~by the laws of physics) and a practitioner seeks the best solution that is compatible with her noisy measurements. Our guiding example is the Fokker-Planck equation, which describes the evolution of density in stochastic diffusion processes. A regression and density estimation framework is introduced for spatio-temporal modeling under Fokker-Planck dynamics with initial and boundary conditions.

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