Kernel Analog Forecasting: Multiscale Test Problems

no code implementations • 13 May 2020 • Dmitry Burov, Dimitrios Giannakis, Krithika Manohar, Andrew Stuart

The nature of the predictions made, and the manner in which they should be interpreted, depends crucially on the extent to which the variables chosen for prediction are Markovian, or approximately Markovian.

An information-geometric approach to feature extraction and moment reconstruction in dynamical systems

no code implementations • 5 Apr 2020 • Suddhasattwa Das, Dimitrios Giannakis, Enikő Székely

One of our main results shows that the evolution of the moments of the dynamics-dependent probability measures can be related to a time-averaging operator on the original dynamical system.

Dimensionality Reduction Time Series Analysis

Reproducing kernel Hilbert space compactification of unitary evolution groups

no code implementations • 4 Aug 2018 • Dimitrios Giannakis, Suddhasattwa Das, Joanna Slawinska

These eigenfunctions can be ordered in terms of a Dirichlet energy on the RKHS, and provide a notion of coherent observables under the dynamics akin to the Koopman eigenfunctions associated with the atomic part of the spectrum.

Time Series Analysis Dynamical Systems 37M99, 37M25, 37A30, 47A60, 28D10, 37A10, 47A35, 37M10