@article{24169, author = {{Nüske, Feliks and Gelß, Patrick and Klus, Stefan and Clementi, Cecilia}}, issn = {{0167-2789}}, journal = {{Physica D: Nonlinear Phenomena}}, title = {{{Tensor-based computation of metastable and coherent sets}}}, doi = {{10.1016/j.physd.2021.133018}}, year = {{2021}}, } @article{16288, abstract = {{We derive a data-driven method for the approximation of the Koopman generator called gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic mode decomposition). This approach is applicable to deterministic and stochastic dynamical systems. It can be used for computing eigenvalues, eigenfunctions, and modes of the generator and for system identification. In addition to learning the governing equations of deterministic systems, which then reduces to SINDy (sparse identification of nonlinear dynamics), it is possible to identify the drift and diffusion terms of stochastic differential equations from data. Moreover, we apply gEDMD to derive coarse-grained models of high-dimensional systems, and also to determine efficient model predictive control strategies. We highlight relationships with other methods and demonstrate the efficacy of the proposed methods using several guiding examples and prototypical molecular dynamics problems.}}, author = {{Klus, Stefan and Nüske, Feliks and Peitz, Sebastian and Niemann, Jan-Hendrik and Clementi, Cecilia and Schütte, Christof}}, issn = {{0167-2789}}, journal = {{Physica D: Nonlinear Phenomena}}, title = {{{Data-driven approximation of the Koopman generator: Model reduction, system identification, and control}}}, doi = {{10.1016/j.physd.2020.132416}}, volume = {{406}}, year = {{2020}}, } @article{16601, author = {{Froyland, Gary and Junge, Oliver and Ochs, Gunter}}, issn = {{0167-2789}}, journal = {{Physica D: Nonlinear Phenomena}}, pages = {{68--84}}, title = {{{Rigorous computation of topological entropy with respect to a finite partition}}}, doi = {{10.1016/s0167-2789(01)00216-0}}, year = {{2001}}, } @article{16518, author = {{Barany, Ernest and Dellnitz, Michael and Golubitsky, Martin}}, issn = {{0167-2789}}, journal = {{Physica D: Nonlinear Phenomena}}, pages = {{66--87}}, title = {{{Detecting the symmetry of attractors}}}, doi = {{10.1016/0167-2789(93)90198-a}}, year = {{1993}}, }