{"title":"Extended Dynamic Mode Decomposition: Sharp bounds on the sample  efficiency","publication":"arXiv:2402.02494","abstract":[{"text":"We rigorously derive novel and sharp finite-data error bounds for highly\r\nsample-efficient Extended Dynamic Mode Decomposition (EDMD) for both i.i.d. and\r\nergodic sampling. In particular, we show all results in a very general setting\r\nremoving most of the typically imposed assumptions such that, among others,\r\ndiscrete- and continuous-time stochastic processes as well as nonlinear partial\r\ndifferential equations are contained in the considered system class. Besides\r\nshowing an exponential rate for i.i.d. sampling, we prove, to the best of our\r\nknowledge, the first superlinear convergence rates for ergodic sampling of\r\ndeterministic systems. We verify sharpness of the derived error bounds by\r\nconducting numerical simulations for highly-complex applications from molecular\r\ndynamics and chaotic flame propagation.","lang":"eng"}],"language":[{"iso":"eng"}],"date_updated":"2024-02-06T08:52:44Z","oa":"1","type":"preprint","citation":{"short":"F.M. Philipp, M. Schaller, S. Boshoff, S. Peitz, F. Nüske, K. Worthmann, ArXiv:2402.02494 (2024).","ama":"Philipp FM, Schaller M, Boshoff S, Peitz S, Nüske F, Worthmann K. Extended Dynamic Mode Decomposition: Sharp bounds on the sample  efficiency. <i>arXiv:240202494</i>. Published online 2024.","ieee":"F. M. Philipp, M. Schaller, S. Boshoff, S. Peitz, F. Nüske, and K. Worthmann, “Extended Dynamic Mode Decomposition: Sharp bounds on the sample  efficiency,” <i>arXiv:2402.02494</i>. 2024.","bibtex":"@article{Philipp_Schaller_Boshoff_Peitz_Nüske_Worthmann_2024, title={Extended Dynamic Mode Decomposition: Sharp bounds on the sample  efficiency}, journal={arXiv:2402.02494}, author={Philipp, Friedrich M. and Schaller, Manuel and Boshoff, Septimus and Peitz, Sebastian and Nüske, Feliks and Worthmann, Karl}, year={2024} }","chicago":"Philipp, Friedrich M., Manuel Schaller, Septimus Boshoff, Sebastian Peitz, Feliks Nüske, and Karl Worthmann. “Extended Dynamic Mode Decomposition: Sharp Bounds on the Sample  Efficiency.” <i>ArXiv:2402.02494</i>, 2024.","mla":"Philipp, Friedrich M., et al. “Extended Dynamic Mode Decomposition: Sharp Bounds on the Sample  Efficiency.” <i>ArXiv:2402.02494</i>, 2024.","apa":"Philipp, F. M., Schaller, M., Boshoff, S., Peitz, S., Nüske, F., &#38; Worthmann, K. (2024). Extended Dynamic Mode Decomposition: Sharp bounds on the sample  efficiency. In <i>arXiv:2402.02494</i>."},"department":[{"_id":"655"}],"date_created":"2024-02-06T08:52:21Z","external_id":{"arxiv":["2402.02494"]},"_id":"51160","status":"public","year":"2024","author":[{"first_name":"Friedrich M.","full_name":"Philipp, Friedrich M.","last_name":"Philipp"},{"first_name":"Manuel","full_name":"Schaller, Manuel","last_name":"Schaller"},{"first_name":"Septimus","full_name":"Boshoff, Septimus","last_name":"Boshoff"},{"last_name":"Peitz","full_name":"Peitz, Sebastian","first_name":"Sebastian","id":"47427","orcid":"0000-0002-3389-793X"},{"first_name":"Feliks","full_name":"Nüske, Feliks","last_name":"Nüske"},{"first_name":"Karl","full_name":"Worthmann, Karl","last_name":"Worthmann"}],"user_id":"47427","main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/2402.02494.pdf"}]}