{rfName}
A

Indexed in

License and use

Icono OpenAccess

Citations

23

Altmetrics

Analysis of institutional authors

Zuazua, EnriqueAuthor

Share

October 6, 2024
Publications
>
Article
Sí

A quantitative analysis of Koopman operator methods for system identification and predictions

Publicated to:COMPTES RENDUS MECANIQUE. 351 (1 S): 1-31 - 2023-01-01 351(1 S), DOI: 10.5802/crmeca.138

Authors: Zhang, Christophe; Zuazua, Enrique

Affiliations

Fdn Deusto, Chair Computat Math, Ave Univ 24, Bilbao 48007, Basque Country, Spain - Author
Friedrich Alexander Univ Erlangen Nurnberg, Dept Data Sci, D-91058 Erlangen, Germany - Author
Univ Autonoma Madrid, Dept Mateat, Madrid 28049, Spain - Author

Abstract

We give convergence and cost estimates for a data-driven system identification method: given an unknown dynamical system, the aim is to recover its vector field and its flow from trajectory data. It is based on the so-called Koopman operator, which uses the well-known link between differential equations and linear transport equations. Data-driven methods recover specific finite-dimensional approximations of the Koopman operator, which can be understood as a transport operator. We focus on such approximations given by classical finite element spaces, which allow us to give estimates on the approximation of the Koopman operator as well as the solutions of the associated linear transport equation. These approximations are thus relevant objects to solve the system identification problem. We then analyze the convergence of a variant of the generator Extended Dynamic Mode Decomposition (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 classical finite element 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 element 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.

Keywords

Data-driven approximationExtended dynamic mode decompositionFinite element spacesKoopman operatorSystem identification

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal COMPTES RENDUS MECANIQUE, and although the journal is classified in the quartile Q4 (Agencia WoS (JCR)), its regional focus and specialization in Mechanics, give it significant recognition in a specific niche of scientific knowledge at an international level.

Independientemente del impacto esperado determinado por el canal de difusión, es importante destacar el impacto real observado de la propia aportación.

Según las diferentes agencias de indexación, el número de citas acumuladas por esta publicación hasta la fecha 2025-07-16:

  • WoS: 5
  • Scopus: 9

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-07-16:

  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 14 (PlumX).

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

  • The work has been submitted to a journal whose editorial policy allows open Open Access publication.
  • Additionally, the work has been submitted to a journal classified as Diamond in relation to this type of editorial policy.

Leadership analysis of institutional authors

This work has been carried out with international collaboration, specifically with researchers from: Germany.

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: Last Author (ZUAZUA IRIONDO, ENRIQUE).