Dynamical Systems Seminar


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 present the construction of different TT representations of tensor-structured data arrays. Furthermore, we also derive efficient algorithms to solve the EDMD eigenvalue problem based on those representations and to project the data into a low-dimensional representation defined by the eigenvectors. We prove that there is a physical interpretation of the procedure and demonstrate its capabilities by applying the method to benchmark data sets of molecular dynamics simulation.

Registration is now closed. Add event to calendar
See all events