BEGIN:VCALENDAR
VERSION:2.0
PRODID:www.imperial.ac.uk
BEGIN:VEVENT
UID:5e8e0e453a747
DTSTART:20200220T130000Z
SEQUENCE:0
TRANSP:OPAQUE
DTEND:20200220T140000Z
URL:https://www.imperial.ac.uk/events/115840/feliks-nuske-paderborn-univers
ity-tensor-based-edmd-for-the-koopman-analysis-of-high-dimensional-systems
/
LOCATION:Room 145\, Huxley Building\, South Kensington Campus\, Imperial Co
llege London\, London\, SW7 2AZ\, United Kingdom
SUMMARY:Feliks Nüske (Paderborn University): Tensor-based EDMD for the Koo
pman analysis of high-dimensional systems
CLASS:PUBLIC
DESCRIPTION:Dynamical Systems Seminar\n\nAbstract:\nRecent years have seen
rapid advances in the data-driven analysis of dynamical systems based on K
oopman operator theory — with extended dynamic mode decomposition (EDMD)
being a cornerstone of the field. On the other hand\, low-rank tensor pro
duct approximations — in particular the tensor train (TT) format — hav
e become a valuable tool for the solution of large-scale problems in a num
ber 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 repre
sentations of tensor-structured data arrays. Furthermore\, we also derive
efficient algorithms to solve the EDMD eigenvalue problem based on those r
epresentations and to project the data into a low-dimensional representati
on defined by the eigenvectors. We prove that there is a physical interpre
tation of the procedure and demonstrate its capabilities by applying the m
ethod to benchmark data sets of molecular dynamics simulation.
X-ALT-DESC;FMTTYPE=text/html:*Dynamical Systems Seminar*

\n\n### Abstract:

\nRecent years have seen rapid advances in th
e data-driven analysis of dynamical systems based on Koopman operator theo
ry — 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 th
is work\, we combine EDMD and the TT format\, enabling the application of
EDMD to high-dimensional problems in conjunction with a large set of featu
res. 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 t
o project the data into a low-dimensional representation defined by the ei
genvectors. We prove that there is a physical interpretation of the proced
ure and demonstrate its capabilities by applying the method to benchmark d
ata sets of molecular dynamics simulation.

DTSTAMP:20200408T174749Z
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