HAVOK Model: A New Perspective on Chaotic Systems with Forcing

This paper introduces the Hankel Alternative View of Koopman operator (HAVOK) model, a novel approach for analyzing chaotic systems with external forcing. The HAVOK model begins by stacking a time series x(t) into a Hankel matrix H. The singular value decomposition (SVD) of H then yields a hierarchy of eigen time series that produce a delay-embedded attractor. A best-fit linear regression model is obtained on the delay coordinates v; the linear fit for the first r-1 variables is excellent, but the last coordinate vr is not well-modeled as linear. Instead, vr(t) is a stochastic input that forces the first r-1 variables. The rare events in the forcing correspond to lobe switching in the chaotic dynamics. This architecture is called the HAVOK model.