  We present a novel kernel-based machine learning algorithm for identifying
the low-dimensional geometry of the effective dynamics of high-dimensional
multiscale stochastic systems. Recently, the authors developed a mathematical
framework for the computation of optimal reaction coordinates of such systems
that is based on learning a parametrization of a low-dimensional transition
manifold in a certain function space. In this article, we enhance this approach
by embedding and learning this transition manifold in a reproducing kernel
Hilbert space, exploiting the favorable properties of kernel embeddings. Under
mild assumptions on the kernel, the manifold structure is shown to be preserved
under the embedding, and distortion bounds can be derived. This leads to a more
robust and more efficient algorithm compared to previous parametrization
approaches.
