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| Kernel methods provide an attractive way of extracting features from data by biasing their geometry in a controlled manner. In this talk, we discuss a family of kernels for dynamical systems featuring an explicit dependence on the dynamical vector field operating in the phase-space manifold, estimated empirically through finite differences of time-ordered data samples. The associated diffusion operator is adapted to the dynamics in that it generates diffusions along the integral curves of the dynamical vector field. We present applications to toy dynamical systems and comprehensive climate models. |
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