Compression of the Koopman matrix for nonlinear physical models via
  hierarchical clustering
Tomoya Nishikata Jun Ohkubo
Machine learning methods allow the prediction of nonlinear dynamical systems
from data alone. The Koopman operator is one of them, which enables us to
employ linear analysis for nonlinear dynamical systems. The linear
characteristics of the Koopman operator are hopeful to understand the nonlinear
dynamics and perform rapid predictions. The extended dynamic mode decomposition
(EDMD) is one of the methods to approximate the Koopman operator as a
finite-dimensional matrix. In this work, we propose a method to compress the
Koopman matrix using hierarchical clustering. Numerical demonstrations for the
cart-pole model and comparisons with the conventional singular value
decomposition (SVD) are shown; the results indicate that the hierarchical
clustering performs better than the naive SVD compressions.