mlsanityData to 7 Oct 2026

Dynamical systems and complex networks: A Koopman operator perspective

arXiv 2405.08940 ↗First posted 14 May 2024math.DS stat.MLcited by 9

Not on the map. Why?

Abstract (arXiv)

The Koopman operator has entered and transformed many research areas over the last years. Although the underlying conceptunicodex2013representing highly nonlinear dynamical systems by infinite-dimensional linear operatorsunicodex2013has been known for a long time, the availability of large data sets and efficient machine learning algorithms for estimating the Koopman operator from data make this framework extremely powerful and popular. Koopman operator theory allows us to gain insights into the characteristic global properties of a system without requiring detailed mathematical models. We will show how these methods can also be used to analyze complex networks and highlight relationships between Koopman operators and graph Laplacians.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 23 of its 95 references that are in the map. First posted on arXiv 14 May 2024.

Builds on

23 of 95 references.

References · 23

  1. 2017VAMPnets: Deep learning of molecular kineticscited by 135
  2. 2016Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive controlcited by 134
  3. 2019Data-driven approximation of the Koopman generator: Model reduction, system identification, and controlcited by 85
  4. 2017Data-driven discovery of Koopman eigenfunctions for controlcited by 64
  5. 2017Eigendecompositions of Transfer Operators in Reproducing Kernel Hilbert Spacescited by 48
  6. 2021Koopman Operator Dynamical Models: Learning, Analysis and Controlcited by 42
  7. 2017Koopman operator-based model reduction for switched-system control of PDEscited by 31
  8. 2020Kernel-based approximation of the Koopman generator and Schr"odinger operatorcited by 31
  9. 2013Sparsity-promoting dynamic mode decompositioncited by 30
  10. 2023The Multiverse of Dynamic Mode Decomposition Algorithmscited by 24
  11. 2016Linear identification of nonlinear systems: A lifting technique based on the Koopman operatorcited by 18
  12. 2020Data-Driven Model Predictive Control using Interpolated Koopman Generatorscited by 17
11 more
  1. 2018Singular Value Decomposition of Operators on Reproducing Kernel Hilbert Spacescited by 14
  2. 2019Kernel methods for detecting coherent structures in dynamical datacited by 13
  3. 2021Robust Tube-based Model Predictive Control with Koopman Operators--Extended Versioncited by 9
  4. 2018A kernel-based approach to molecular conformation analysiscited by 8
  5. 2022Koopman-based spectral clustering of directed and time-evolving graphscited by 6
  6. 2019Tensor-based computation of metastable and coherent setscited by 4
  7. 2023Transfer operators on graphs: Spectral clustering and beyondcited by 3
  8. 2024Broken detailed balance and entropy production in directed networkscited by 3
  9. 2020Data-driven model reduction of agent-based systems using the Koopman generatorcited by 2
  10. 2014Modularity of Directed Networks: Cycle Decomposition Approachcited by 1
  11. 2022Data-driven Influence Based Clustering of Dynamical Systemscited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 4; 2026: 4.

9 papers.

  1. 2025Learning graphons from data: Random walks, transfer operators, and spectral clusteringcited by 2
  2. 2025How deep is your network? Deep vs. shallow learning of transfer operatorscited by 2
  3. 2024Clustering Time-Evolving Networks Using the Spatio-Temporal Graph Laplaciancited by 1
  4. 2025Data-driven system identification using quadratic embeddings of nonlinear dynamicscited by 1
  5. 2025Data-driven approximation of transfer operators for mean-field stochastic differential equationscited by 0
  6. 2026Taming Epilepsy: Mean Field Control of Whole-Brain Dynamicscited by 0
  7. 2026Optimization of randomized neural networks for transfer operator approximationcited by 0
  8. 2026Integral Formulation of QENDy for Robust Nonlinear System Identificationcited by 0
  9. 2026Functional dynamic mode decomposition: Learning infinite-dimensional systems from datacited by 0