2 research outputs found
Tensor-based computation of metastable and coherent sets
Recent years have seen rapid advances in the data-driven analysis of
dynamical systems based on Koopman operator theory -- with extended dynamic
mode decomposition (EDMD) being a cornerstone of the field. On the other hand,
low-rank tensor product approximations -- in particular the tensor train (TT)
format -- have become a valuable tool for the solution of large-scale problems
in a number of fields. In this work, we combine EDMD and the TT format,
enabling the application of EDMD to high-dimensional problems in conjunction
with a large set of features. We derive efficient algorithms to solve the EDMD
eigenvalue problem based on tensor representations of the data, and to project
the data into a low-dimensional representation defined by the eigenvectors. We
extend this method to perform canonical correlation analysis (CCA) of
non-reversible or time-dependent systems. We prove that there is a physical
interpretation of the procedure and demonstrate its capabilities by applying
the method to several benchmark data sets