We then analyze the convergence of a variant of the generator Extended Dynamic Mode Decom-
position (gEDMD) algorithm, one of the main algorithms developed to compute approximations of
the Koopman operator from data. We find however that, when combining this algorithm with clas-
sical finite elements spaces, the results are not satisfactory numerically, as the convergence of the
data-driven approximation is too slow for the method to benefit from the accuracy of finite elements
spaces. In particular, for problems in dimension 1 it is less efficient than direct interpolation methods
to recover the vector field. We provide some numerical examples to illustrate this last point.

},
author = {Zhang, Christophe and Zuazua Iriondo, Enrique},
doi = {10.5802/crmeca.138},
faupublication = {yes},
journal = {Comptes Rendus Mecanique},
keywords = {Koopman operator; system identification; finite elements spaces; data-driven approximation; Extended Dynamic Mode Decomposition},
pages = {1-31},
peerreviewed = {Yes},
title = {{A} quantitative analysis of {Koopman} operator methods for system identification and predictions},
url = {https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.138/},
volume = {351},
year = {2023}
}
@article{faucris.268915153,
abstract = {We use a variant the backstepping method to study the stabilization of a 1-D linear transport equation on the interval (0, L), by controlling the scalar amplitude of a piecewise regular function of the space variable in the source term. We prove that if the system is controllable in a periodic Sobolev space of order greater than 1, then the system can be stabilized exponentially in that space and, for any given decay rate, we give an explicit feedback law that achieves that decay rate. The variant of the backstepping method used here relies mainly on the spectral properties of the linear transport equation, and leads to some original technical developments that differ substantially from previous applications.},
author = {Zhang, Christophe},
doi = {10.3934/mcrf.2021006},
faupublication = {yes},
journal = {Mathematical Control and Related Fields},
keywords = {Backstepping; Fredholm transformations; Internal control; Rapid stabilization; Stabilization; System equivalence; Transport equation},
note = {CRIS-Team Scopus Importer:2022-02-04},
pages = {169-200},
peerreviewed = {Yes},
title = {{INTERNAL} {RAPID} {STABILIZATION} {OF} {A} 1-{D} {LINEAR} {TRANSPORT} {EQUATION} {WITH} {A} {SCALAR} {FEEDBACK}},
volume = {12},
year = {2022}
}