Schütte, Christof; Klus, Stefan; Hartmann, Carsten Overcoming the timescale barrier in molecular dynamics: transfer operators, variational principles and machine learning. (English) Zbl 07736659 Acta Numerica 32, 517-673 (2023). MSC: 65-XX 37M10 37M25 82C31 82M37 47D07 60J35 60J60 PDFBibTeX XMLCite \textit{C. Schütte} et al., Acta Numerica 32, 517--673 (2023; Zbl 07736659) Full Text: DOI
Lücke, Marvin; Nüske, Feliks tgEDMD: approximation of the Kolmogorov operator in tensor train format. (English) Zbl 1500.37046 J. Nonlinear Sci. 32, No. 4, Paper No. 44, 30 p. (2022). MSC: 37M10 37M05 60H10 65F55 82B31 PDFBibTeX XMLCite \textit{M. Lücke} and \textit{F. Nüske}, J. Nonlinear Sci. 32, No. 4, Paper No. 44, 30 p. (2022; Zbl 1500.37046) Full Text: DOI arXiv
Tian, Wenchong; Wu, Hao Kernel embedding based variational approach for low-dimensional approximation of dynamical systems. (English) Zbl 1482.37087 Comput. Methods Appl. Math. 21, No. 3, 635-659 (2021). MSC: 37M10 37L65 47N30 65K10 PDFBibTeX XMLCite \textit{W. Tian} and \textit{H. Wu}, Comput. Methods Appl. Math. 21, No. 3, 635--659 (2021; Zbl 1482.37087) Full Text: DOI arXiv
Kamb, Mason; Kaiser, Eurika; Brunton, Steven L.; Kutz, J. Nathan Time-delay observables for Koopman: theory and applications. (English) Zbl 1441.37090 SIAM J. Appl. Dyn. Syst. 19, No. 2, 886-917 (2020). MSC: 37M10 37N30 PDFBibTeX XMLCite \textit{M. Kamb} et al., SIAM J. Appl. Dyn. Syst. 19, No. 2, 886--917 (2020; Zbl 1441.37090) Full Text: DOI arXiv
Wu, Hao; Noé, Frank Variational approach for learning Markov processes from time series data. (English) Zbl 1437.37107 J. Nonlinear Sci. 30, No. 1, 23-66 (2020). MSC: 37M10 47N30 65K10 60J22 PDFBibTeX XMLCite \textit{H. Wu} and \textit{F. Noé}, J. Nonlinear Sci. 30, No. 1, 23--66 (2020; Zbl 1437.37107) Full Text: DOI arXiv
Rudy, Samuel H.; Nathan Kutz, J.; Brunton, Steven L. Deep learning of dynamics and signal-noise decomposition with time-stepping constraints. (English) Zbl 1452.68170 J. Comput. Phys. 396, 483-506 (2019). MSC: 68T07 34C28 34C60 37M10 PDFBibTeX XMLCite \textit{S. H. Rudy} et al., J. Comput. Phys. 396, 483--506 (2019; Zbl 1452.68170) Full Text: DOI arXiv
Qin, Tong; Wu, Kailiang; Xiu, Dongbin Data driven governing equations approximation using deep neural networks. (English) Zbl 1455.65125 J. Comput. Phys. 395, 620-635 (2019). MSC: 65L99 37C10 37M10 68T07 PDFBibTeX XMLCite \textit{T. Qin} et al., J. Comput. Phys. 395, 620--635 (2019; Zbl 1455.65125) Full Text: DOI arXiv
Klus, Stefan; Husic, Brooke E.; Mollenhauer, Mattes; Noé, Frank Kernel methods for detecting coherent structures in dynamical data. (English) Zbl 1448.37100 Chaos 29, No. 12, 123112, 15 p. (2019). MSC: 37M10 37M05 PDFBibTeX XMLCite \textit{S. Klus} et al., Chaos 29, No. 12, 123112, 15 p. (2019; Zbl 1448.37100) Full Text: DOI arXiv
Champion, Kathleen P.; Brunton, Steven L.; Kutz, J. Nathan Discovery of nonlinear multiscale systems: sampling strategies and embeddings. (English) Zbl 1474.65476 SIAM J. Appl. Dyn. Syst. 18, No. 1, 312-333 (2019). MSC: 65P99 37M10 37N10 62K99 15B99 PDFBibTeX XMLCite \textit{K. P. Champion} et al., SIAM J. Appl. Dyn. Syst. 18, No. 1, 312--333 (2019; Zbl 1474.65476) Full Text: DOI arXiv