Speaker
Description
We present a method combining ideas from the theory of vector-valued
kernels with delay-coordinate embedding techniques in dynamical systems
capable of identifying spatiotemporal patterns, without prior knowledge of the
state space or the dynamical laws of the system generating the data. The
approach is particularly powerful for systems in which characteristic patterns
cannot be readily decomposed into temporal and spatial coordinates and are
characterized by wide range of scales, potentially coupled with each other.
We show our approach reveals coherent patterns of intermittent character
with significantly higher skill than conventional analytical methods based on
decomposing signals into separable spatial and temporal patterns. Our
approach employs Koopman operator theory and its data-driven
approximation with novel machine learning approaches. Extensions of our
techniques to nonparameteric predictions, including data-assimilation and
subgrid-scale modeling, will be presented as well. Applications in
heliophysics and astrophysics will be discussed in the end.
