[{"date_created":"2021-04-19T16:17:30Z","type":"preprint","department":[{"_id":"101"}],"oa":"1","publication":"arXiv:1804.00854","citation":{"ama":"Hanke S, Peitz S, Wallscheid O, Klus S, Böcker J, Dellnitz M. Koopman Operator-Based Finite-Control-Set Model Predictive Control for  Electrical Drives. <i>arXiv:180400854</i>. 2018.","bibtex":"@article{Hanke_Peitz_Wallscheid_Klus_Böcker_Dellnitz_2018, title={Koopman Operator-Based Finite-Control-Set Model Predictive Control for  Electrical Drives}, journal={arXiv:1804.00854}, author={Hanke, Sören and Peitz, Sebastian and Wallscheid, Oliver and Klus, Stefan and Böcker, Joachim and Dellnitz, Michael}, year={2018} }","mla":"Hanke, Sören, et al. “Koopman Operator-Based Finite-Control-Set Model Predictive Control for  Electrical Drives.” <i>ArXiv:1804.00854</i>, 2018.","chicago":"Hanke, Sören, Sebastian Peitz, Oliver Wallscheid, Stefan Klus, Joachim Böcker, and Michael Dellnitz. “Koopman Operator-Based Finite-Control-Set Model Predictive Control for  Electrical Drives.” <i>ArXiv:1804.00854</i>, 2018.","short":"S. Hanke, S. Peitz, O. Wallscheid, S. Klus, J. Böcker, M. Dellnitz, ArXiv:1804.00854 (2018).","apa":"Hanke, S., Peitz, S., Wallscheid, O., Klus, S., Böcker, J., &#38; Dellnitz, M. (2018). Koopman Operator-Based Finite-Control-Set Model Predictive Control for  Electrical Drives. <i>ArXiv:1804.00854</i>.","ieee":"S. Hanke, S. Peitz, O. Wallscheid, S. Klus, J. Böcker, and M. Dellnitz, “Koopman Operator-Based Finite-Control-Set Model Predictive Control for  Electrical Drives,” <i>arXiv:1804.00854</i>. 2018."},"abstract":[{"lang":"eng","text":"Predictive control of power electronic systems always requires a suitable\r\nmodel of the plant. Using typical physics-based white box models, a trade-off\r\nbetween model complexity (i.e. accuracy) and computational burden has to be\r\nmade. This is a challenging task with a lot of constraints, since the model\r\norder is directly linked to the number of system states. Even though white-box\r\nmodels show suitable performance in most cases, parasitic real-world effects\r\noften cannot be modeled satisfactorily with an expedient computational load.\r\nHence, a Koopman operator-based model reduction technique is presented which\r\ndirectly links the control action to the system's outputs in a black-box\r\nfashion. The Koopman operator is a linear but infinite-dimensional operator\r\ndescribing the dynamics of observables of nonlinear autonomous dynamical\r\nsystems which can be nicely applied to the switching principle of power\r\nelectronic devices. Following this data-driven approach, the model order and\r\nthe number of system states are decoupled which allows us to consider more\r\ncomplex systems. Extensive experimental tests with an automotive-type permanent\r\nmagnet synchronous motor fed by an IGBT 2-level inverter prove the feasibility\r\nof the proposed modeling technique in a finite-set model predictive control\r\napplication."}],"main_file_link":[{"url":"https://arxiv.org/pdf/1804.00854.pdf","open_access":"1"}],"language":[{"iso":"eng"}],"_id":"21634","user_id":"47427","title":"Koopman Operator-Based Finite-Control-Set Model Predictive Control for  Electrical Drives","year":"2018","status":"public","author":[{"full_name":"Hanke, Sören","last_name":"Hanke","first_name":"Sören"},{"full_name":"Peitz, Sebastian","first_name":"Sebastian","orcid":"0000-0002-3389-793X","last_name":"Peitz","id":"47427"},{"first_name":"Oliver","last_name":"Wallscheid","full_name":"Wallscheid, Oliver"},{"last_name":"Klus","first_name":"Stefan","full_name":"Klus, Stefan"},{"full_name":"Böcker, Joachim","last_name":"Böcker","first_name":"Joachim"},{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"}],"date_updated":"2022-01-06T06:55:08Z"},{"date_created":"2021-04-30T16:58:07Z","type":"journal_article","department":[{"_id":"101"}],"publication":"Journal of Chemical Theory and Computation","citation":{"ieee":"F. Litzinger <i>et al.</i>, “Rapid Calculation of Molecular Kinetics Using Compressed Sensing,” <i>Journal of Chemical Theory and Computation</i>, pp. 2771–2783, 2018.","apa":"Litzinger, F., Boninsegna, L., Wu, H., Nüske, F., Patel, R., Baraniuk, R., … Clementi, C. (2018). Rapid Calculation of Molecular Kinetics Using Compressed Sensing. <i>Journal of Chemical Theory and Computation</i>, 2771–2783. <a href=\"https://doi.org/10.1021/acs.jctc.8b00089\">https://doi.org/10.1021/acs.jctc.8b00089</a>","short":"F. Litzinger, L. Boninsegna, H. Wu, F. Nüske, R. Patel, R. Baraniuk, F. Noé, C. Clementi, Journal of Chemical Theory and Computation (2018) 2771–2783.","chicago":"Litzinger, Florian, Lorenzo Boninsegna, Hao Wu, Feliks Nüske, Raajen Patel, Richard Baraniuk, Frank Noé, and Cecilia Clementi. “Rapid Calculation of Molecular Kinetics Using Compressed Sensing.” <i>Journal of Chemical Theory and Computation</i>, 2018, 2771–83. <a href=\"https://doi.org/10.1021/acs.jctc.8b00089\">https://doi.org/10.1021/acs.jctc.8b00089</a>.","mla":"Litzinger, Florian, et al. “Rapid Calculation of Molecular Kinetics Using Compressed Sensing.” <i>Journal of Chemical Theory and Computation</i>, 2018, pp. 2771–83, doi:<a href=\"https://doi.org/10.1021/acs.jctc.8b00089\">10.1021/acs.jctc.8b00089</a>.","bibtex":"@article{Litzinger_Boninsegna_Wu_Nüske_Patel_Baraniuk_Noé_Clementi_2018, title={Rapid Calculation of Molecular Kinetics Using Compressed Sensing}, DOI={<a href=\"https://doi.org/10.1021/acs.jctc.8b00089\">10.1021/acs.jctc.8b00089</a>}, journal={Journal of Chemical Theory and Computation}, author={Litzinger, Florian and Boninsegna, Lorenzo and Wu, Hao and Nüske, Feliks and Patel, Raajen and Baraniuk, Richard and Noé, Frank and Clementi, Cecilia}, year={2018}, pages={2771–2783} }","ama":"Litzinger F, Boninsegna L, Wu H, et al. Rapid Calculation of Molecular Kinetics Using Compressed Sensing. <i>Journal of Chemical Theory and Computation</i>. 2018:2771-2783. doi:<a href=\"https://doi.org/10.1021/acs.jctc.8b00089\">10.1021/acs.jctc.8b00089</a>"},"extern":"1","page":"2771-2783","_id":"21940","language":[{"iso":"eng"}],"user_id":"81513","doi":"10.1021/acs.jctc.8b00089","title":"Rapid Calculation of Molecular Kinetics Using Compressed Sensing","status":"public","year":"2018","author":[{"full_name":"Litzinger, Florian","first_name":"Florian","last_name":"Litzinger"},{"full_name":"Boninsegna, Lorenzo","last_name":"Boninsegna","first_name":"Lorenzo"},{"last_name":"Wu","first_name":"Hao","full_name":"Wu, Hao"},{"id":"81513","last_name":"Nüske","first_name":"Feliks","orcid":"0000-0003-2444-7889","full_name":"Nüske, Feliks"},{"first_name":"Raajen","last_name":"Patel","full_name":"Patel, Raajen"},{"full_name":"Baraniuk, Richard","first_name":"Richard","last_name":"Baraniuk"},{"full_name":"Noé, Frank","first_name":"Frank","last_name":"Noé"},{"first_name":"Cecilia","last_name":"Clementi","full_name":"Clementi, Cecilia"}],"publication_identifier":{"issn":["1549-9618","1549-9626"]},"publication_status":"published","date_updated":"2022-01-06T06:55:20Z"},{"status":"public","year":"2018","title":"Data-Driven Model Reduction and Transfer Operator Approximation","author":[{"full_name":"Klus, Stefan","first_name":"Stefan","last_name":"Klus"},{"first_name":"Feliks","orcid":"0000-0003-2444-7889","last_name":"Nüske","full_name":"Nüske, Feliks","id":"81513"},{"full_name":"Koltai, Péter","last_name":"Koltai","first_name":"Péter"},{"last_name":"Wu","first_name":"Hao","full_name":"Wu, Hao"},{"last_name":"Kevrekidis","first_name":"Ioannis","full_name":"Kevrekidis, Ioannis"},{"full_name":"Schütte, Christof","last_name":"Schütte","first_name":"Christof"},{"first_name":"Frank","last_name":"Noé","full_name":"Noé, Frank"}],"publication_identifier":{"issn":["0938-8974","1432-1467"]},"publication_status":"published","date_updated":"2022-01-06T06:55:20Z","page":"985-1010","_id":"21941","language":[{"iso":"eng"}],"user_id":"81513","doi":"10.1007/s00332-017-9437-7","publication":"Journal of Nonlinear Science","citation":{"mla":"Klus, Stefan, et al. “Data-Driven Model Reduction and Transfer Operator Approximation.” <i>Journal of Nonlinear Science</i>, 2018, pp. 985–1010, doi:<a href=\"https://doi.org/10.1007/s00332-017-9437-7\">10.1007/s00332-017-9437-7</a>.","ama":"Klus S, Nüske F, Koltai P, et al. Data-Driven Model Reduction and Transfer Operator Approximation. <i>Journal of Nonlinear Science</i>. 2018:985-1010. doi:<a href=\"https://doi.org/10.1007/s00332-017-9437-7\">10.1007/s00332-017-9437-7</a>","bibtex":"@article{Klus_Nüske_Koltai_Wu_Kevrekidis_Schütte_Noé_2018, title={Data-Driven Model Reduction and Transfer Operator Approximation}, DOI={<a href=\"https://doi.org/10.1007/s00332-017-9437-7\">10.1007/s00332-017-9437-7</a>}, journal={Journal of Nonlinear Science}, author={Klus, Stefan and Nüske, Feliks and Koltai, Péter and Wu, Hao and Kevrekidis, Ioannis and Schütte, Christof and Noé, Frank}, year={2018}, pages={985–1010} }","apa":"Klus, S., Nüske, F., Koltai, P., Wu, H., Kevrekidis, I., Schütte, C., &#38; Noé, F. (2018). Data-Driven Model Reduction and Transfer Operator Approximation. <i>Journal of Nonlinear Science</i>, 985–1010. <a href=\"https://doi.org/10.1007/s00332-017-9437-7\">https://doi.org/10.1007/s00332-017-9437-7</a>","ieee":"S. Klus <i>et al.</i>, “Data-Driven Model Reduction and Transfer Operator Approximation,” <i>Journal of Nonlinear Science</i>, pp. 985–1010, 2018.","chicago":"Klus, Stefan, Feliks Nüske, Péter Koltai, Hao Wu, Ioannis Kevrekidis, Christof Schütte, and Frank Noé. “Data-Driven Model Reduction and Transfer Operator Approximation.” <i>Journal of Nonlinear Science</i>, 2018, 985–1010. <a href=\"https://doi.org/10.1007/s00332-017-9437-7\">https://doi.org/10.1007/s00332-017-9437-7</a>.","short":"S. Klus, F. Nüske, P. Koltai, H. Wu, I. Kevrekidis, C. Schütte, F. Noé, Journal of Nonlinear Science (2018) 985–1010."},"extern":"1","date_created":"2021-04-30T16:59:03Z","type":"journal_article","department":[{"_id":"101"}]},{"publication_status":"published","date_updated":"2022-01-06T06:55:20Z","title":"Sparse learning of stochastic dynamical equations","status":"public","year":"2018","publication_identifier":{"issn":["0021-9606","1089-7690"]},"author":[{"full_name":"Boninsegna, Lorenzo","last_name":"Boninsegna","first_name":"Lorenzo"},{"full_name":"Nüske, Feliks","last_name":"Nüske","first_name":"Feliks","orcid":"0000-0003-2444-7889","id":"81513"},{"full_name":"Clementi, Cecilia","last_name":"Clementi","first_name":"Cecilia"}],"user_id":"81513","doi":"10.1063/1.5018409","article_number":"241723","language":[{"iso":"eng"}],"_id":"21942","extern":"1","publication":"The Journal of Chemical Physics","citation":{"mla":"Boninsegna, Lorenzo, et al. “Sparse Learning of Stochastic Dynamical Equations.” <i>The Journal of Chemical Physics</i>, 241723, 2018, doi:<a href=\"https://doi.org/10.1063/1.5018409\">10.1063/1.5018409</a>.","ama":"Boninsegna L, Nüske F, Clementi C. Sparse learning of stochastic dynamical equations. <i>The Journal of Chemical Physics</i>. 2018. doi:<a href=\"https://doi.org/10.1063/1.5018409\">10.1063/1.5018409</a>","bibtex":"@article{Boninsegna_Nüske_Clementi_2018, title={Sparse learning of stochastic dynamical equations}, DOI={<a href=\"https://doi.org/10.1063/1.5018409\">10.1063/1.5018409</a>}, number={241723}, journal={The Journal of Chemical Physics}, author={Boninsegna, Lorenzo and Nüske, Feliks and Clementi, Cecilia}, year={2018} }","apa":"Boninsegna, L., Nüske, F., &#38; Clementi, C. (2018). Sparse learning of stochastic dynamical equations. <i>The Journal of Chemical Physics</i>. <a href=\"https://doi.org/10.1063/1.5018409\">https://doi.org/10.1063/1.5018409</a>","ieee":"L. Boninsegna, F. Nüske, and C. Clementi, “Sparse learning of stochastic dynamical equations,” <i>The Journal of Chemical Physics</i>, 2018.","chicago":"Boninsegna, Lorenzo, Feliks Nüske, and Cecilia Clementi. “Sparse Learning of Stochastic Dynamical Equations.” <i>The Journal of Chemical Physics</i>, 2018. <a href=\"https://doi.org/10.1063/1.5018409\">https://doi.org/10.1063/1.5018409</a>.","short":"L. Boninsegna, F. Nüske, C. Clementi, The Journal of Chemical Physics (2018)."},"type":"journal_article","department":[{"_id":"101"}],"date_created":"2021-04-30T16:59:39Z"},{"publication":"The Journal of Chemical Physics","citation":{"mla":"Hruska, Eugen, et al. “Quantitative Comparison of Adaptive Sampling Methods for Protein Dynamics.” <i>The Journal of Chemical Physics</i>, 244119, 2018, doi:<a href=\"https://doi.org/10.1063/1.5053582\">10.1063/1.5053582</a>.","apa":"Hruska, E., Abella, J. R., Nüske, F., Kavraki, L. E., &#38; Clementi, C. (2018). Quantitative comparison of adaptive sampling methods for protein dynamics. <i>The Journal of Chemical Physics</i>. <a href=\"https://doi.org/10.1063/1.5053582\">https://doi.org/10.1063/1.5053582</a>","ieee":"E. Hruska, J. R. Abella, F. Nüske, L. E. Kavraki, and C. Clementi, “Quantitative comparison of adaptive sampling methods for protein dynamics,” <i>The Journal of Chemical Physics</i>, 2018.","chicago":"Hruska, Eugen, Jayvee R. Abella, Feliks Nüske, Lydia E. Kavraki, and Cecilia Clementi. “Quantitative Comparison of Adaptive Sampling Methods for Protein Dynamics.” <i>The Journal of Chemical Physics</i>, 2018. <a href=\"https://doi.org/10.1063/1.5053582\">https://doi.org/10.1063/1.5053582</a>.","short":"E. Hruska, J.R. Abella, F. Nüske, L.E. Kavraki, C. Clementi, The Journal of Chemical Physics (2018).","ama":"Hruska E, Abella JR, Nüske F, Kavraki LE, Clementi C. Quantitative comparison of adaptive sampling methods for protein dynamics. <i>The Journal of Chemical Physics</i>. 2018. doi:<a href=\"https://doi.org/10.1063/1.5053582\">10.1063/1.5053582</a>","bibtex":"@article{Hruska_Abella_Nüske_Kavraki_Clementi_2018, title={Quantitative comparison of adaptive sampling methods for protein dynamics}, DOI={<a href=\"https://doi.org/10.1063/1.5053582\">10.1063/1.5053582</a>}, number={244119}, journal={The Journal of Chemical Physics}, author={Hruska, Eugen and Abella, Jayvee R. and Nüske, Feliks and Kavraki, Lydia E. and Clementi, Cecilia}, year={2018} }"},"extern":"1","date_created":"2021-04-30T17:00:24Z","type":"journal_article","department":[{"_id":"101"}],"year":"2018","title":"Quantitative comparison of adaptive sampling methods for protein dynamics","status":"public","publication_identifier":{"issn":["0021-9606","1089-7690"]},"author":[{"full_name":"Hruska, Eugen","first_name":"Eugen","last_name":"Hruska"},{"first_name":"Jayvee R.","last_name":"Abella","full_name":"Abella, Jayvee R."},{"orcid":"0000-0003-2444-7889","first_name":"Feliks","last_name":"Nüske","full_name":"Nüske, Feliks","id":"81513"},{"last_name":"Kavraki","first_name":"Lydia E.","full_name":"Kavraki, Lydia E."},{"full_name":"Clementi, Cecilia","last_name":"Clementi","first_name":"Cecilia"}],"date_updated":"2022-01-06T06:55:20Z","publication_status":"published","article_number":"244119","_id":"21943","language":[{"iso":"eng"}],"doi":"10.1063/1.5053582","user_id":"81513"},{"abstract":[{"text":"In this article we propose a descent method for equality and inequality constrained multiobjective optimization problems (MOPs) which generalizes the steepest descent method for unconstrained MOPs by Fliege and Svaiter to constrained problems by using two active set strategies. Under some regularity assumptions on the problem, we show that accumulation points of our descent method satisfy a necessary condition for local Pareto optimality. Finally, we show the typical behavior of our method in a numerical example.","lang":"eng"}],"citation":{"bibtex":"@inproceedings{Gebken_Peitz_Dellnitz_2018, place={Cham}, title={A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems}, DOI={<a href=\"https://doi.org/10.1007/978-3-319-96104-0_2\">10.1007/978-3-319-96104-0_2</a>}, booktitle={Numerical and Evolutionary Optimization – NEO 2017}, author={Gebken, Bennet and Peitz, Sebastian and Dellnitz, Michael}, year={2018} }","ama":"Gebken B, Peitz S, Dellnitz M. A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems. In: <i>Numerical and Evolutionary Optimization – NEO 2017</i>. Cham; 2018. doi:<a href=\"https://doi.org/10.1007/978-3-319-96104-0_2\">10.1007/978-3-319-96104-0_2</a>","mla":"Gebken, Bennet, et al. “A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems.” <i>Numerical and Evolutionary Optimization – NEO 2017</i>, 2018, doi:<a href=\"https://doi.org/10.1007/978-3-319-96104-0_2\">10.1007/978-3-319-96104-0_2</a>.","short":"B. Gebken, S. Peitz, M. Dellnitz, in: Numerical and Evolutionary Optimization – NEO 2017, Cham, 2018.","chicago":"Gebken, Bennet, Sebastian Peitz, and Michael Dellnitz. “A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems.” In <i>Numerical and Evolutionary Optimization – NEO 2017</i>. Cham, 2018. <a href=\"https://doi.org/10.1007/978-3-319-96104-0_2\">https://doi.org/10.1007/978-3-319-96104-0_2</a>.","ieee":"B. Gebken, S. Peitz, and M. Dellnitz, “A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems,” in <i>Numerical and Evolutionary Optimization – NEO 2017</i>, 2018.","apa":"Gebken, B., Peitz, S., &#38; Dellnitz, M. (2018). A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems. In <i>Numerical and Evolutionary Optimization – NEO 2017</i>. Cham. <a href=\"https://doi.org/10.1007/978-3-319-96104-0_2\">https://doi.org/10.1007/978-3-319-96104-0_2</a>"},"publication":"Numerical and Evolutionary Optimization – NEO 2017","department":[{"_id":"101"}],"type":"conference","date_created":"2019-03-29T13:26:47Z","place":"Cham","publication_status":"published","date_updated":"2022-01-06T07:04:00Z","publication_identifier":{"isbn":["9783319961033","9783319961040"],"issn":["1860-949X","1860-9503"]},"author":[{"id":"32643","full_name":"Gebken, Bennet","last_name":"Gebken","first_name":"Bennet"},{"full_name":"Peitz, Sebastian","first_name":"Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","id":"47427"},{"full_name":"Dellnitz, Michael","first_name":"Michael","last_name":"Dellnitz"}],"conference":{"name":"NEO 2017: Numerical and Evolutionary Optimization"},"status":"public","title":"A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems","year":"2018","user_id":"47427","doi":"10.1007/978-3-319-96104-0_2","language":[{"iso":"eng"}],"_id":"8750"},{"citation":{"mla":"Peitz, Sebastian, and Michael Dellnitz. “A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction.” <i>Mathematical and Computational Applications</i>, vol. 23, no. 2, 2018, doi:<a href=\"https://doi.org/10.3390/mca23020030\">10.3390/mca23020030</a>.","bibtex":"@article{Peitz_Dellnitz_2018, title={A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction}, volume={23}, DOI={<a href=\"https://doi.org/10.3390/mca23020030\">10.3390/mca23020030</a>}, number={2}, journal={Mathematical and Computational Applications}, author={Peitz, Sebastian and Dellnitz, Michael}, year={2018} }","ama":"Peitz S, Dellnitz M. A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction. <i>Mathematical and Computational Applications</i>. 2018;23(2). doi:<a href=\"https://doi.org/10.3390/mca23020030\">10.3390/mca23020030</a>","ieee":"S. Peitz and M. Dellnitz, “A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction,” <i>Mathematical and Computational Applications</i>, vol. 23, no. 2, 2018.","apa":"Peitz, S., &#38; Dellnitz, M. (2018). A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction. <i>Mathematical and Computational Applications</i>, <i>23</i>(2). <a href=\"https://doi.org/10.3390/mca23020030\">https://doi.org/10.3390/mca23020030</a>","chicago":"Peitz, Sebastian, and Michael Dellnitz. “A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction.” <i>Mathematical and Computational Applications</i> 23, no. 2 (2018). <a href=\"https://doi.org/10.3390/mca23020030\">https://doi.org/10.3390/mca23020030</a>.","short":"S. Peitz, M. Dellnitz, Mathematical and Computational Applications 23 (2018)."},"oa":"1","status":"public","user_id":"47427","volume":23,"_id":"8751","abstract":[{"lang":"eng","text":"Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control, which results in new challenges such as expensive models or real-time applicability. Since the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in accelerating multiobjective optimal control for complex problems where either PDE constraints are present or where a feedback behavior has to be achieved. In the first case, surrogate models yield significant speed-ups. Besides classical meta-modeling techniques for multiobjective optimization, a promising alternative for control problems is to introduce a surrogate model for the system dynamics. In the case of real-time requirements, various promising model predictive control approaches have been proposed, using either fast online solvers or offline-online decomposition. We also briefly comment on dimension reduction in many-objective optimization problems as another technique for reducing the numerical effort."}],"issue":"2","publication":"Mathematical and Computational Applications","type":"journal_article","department":[{"_id":"101"}],"date_created":"2019-03-29T13:27:51Z","publication_status":"published","date_updated":"2022-01-06T07:04:00Z","article_type":"review","intvolume":"        23","year":"2018","title":"A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction","publication_identifier":{"issn":["2297-8747"]},"author":[{"first_name":"Sebastian","last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian","id":"47427"},{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"}],"doi":"10.3390/mca23020030","main_file_link":[{"url":"https://www.mdpi.com/2297-8747/23/2/30/pdf","open_access":"1"}],"language":[{"iso":"eng"}]},{"department":[{"_id":"101"}],"type":"book_chapter","date_created":"2019-03-29T13:31:20Z","place":"Cham","project":[{"_id":"52","name":"Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"abstract":[{"text":"In this chapter, we combine a global, derivative-free subdivision algorithm for multiobjective optimization problems with a posteriori error estimates for reduced-order models based on Proper Orthogonal Decomposition in order to efficiently solve multiobjective optimization problems governed by partial differential equations. An error bound for a semilinear heat equation is developed in such a way that the errors in the conflicting objectives can be estimated individually. The resulting algorithm constructs a library of locally valid reduced-order models online using a Greedy (worst-first) search. Using this approach, the number of evaluations of the full-order model can be reduced by a factor of more than 1000.","lang":"eng"}],"citation":{"mla":"Beermann, Dennis, et al. “Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition.” <i>Reduced-Order Modeling (ROM) for Simulation and Optimization</i>, 2018, pp. 47–72, doi:<a href=\"https://doi.org/10.1007/978-3-319-75319-5_3\">10.1007/978-3-319-75319-5_3</a>.","ama":"Beermann D, Dellnitz M, Peitz S, Volkwein S. Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition. In: <i>Reduced-Order Modeling (ROM) for Simulation and Optimization</i>. Cham; 2018:47-72. doi:<a href=\"https://doi.org/10.1007/978-3-319-75319-5_3\">10.1007/978-3-319-75319-5_3</a>","bibtex":"@inbook{Beermann_Dellnitz_Peitz_Volkwein_2018, place={Cham}, title={Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition}, DOI={<a href=\"https://doi.org/10.1007/978-3-319-75319-5_3\">10.1007/978-3-319-75319-5_3</a>}, booktitle={Reduced-Order Modeling (ROM) for Simulation and Optimization}, author={Beermann, Dennis and Dellnitz, Michael and Peitz, Sebastian and Volkwein, Stefan}, year={2018}, pages={47–72} }","apa":"Beermann, D., Dellnitz, M., Peitz, S., &#38; Volkwein, S. (2018). Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition. In <i>Reduced-Order Modeling (ROM) for Simulation and Optimization</i> (pp. 47–72). Cham. <a href=\"https://doi.org/10.1007/978-3-319-75319-5_3\">https://doi.org/10.1007/978-3-319-75319-5_3</a>","ieee":"D. Beermann, M. Dellnitz, S. Peitz, and S. Volkwein, “Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition,” in <i>Reduced-Order Modeling (ROM) for Simulation and Optimization</i>, Cham, 2018, pp. 47–72.","short":"D. Beermann, M. Dellnitz, S. Peitz, S. Volkwein, in: Reduced-Order Modeling (ROM) for Simulation and Optimization, Cham, 2018, pp. 47–72.","chicago":"Beermann, Dennis, Michael Dellnitz, Sebastian Peitz, and Stefan Volkwein. “Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition.” In <i>Reduced-Order Modeling (ROM) for Simulation and Optimization</i>, 47–72. Cham, 2018. <a href=\"https://doi.org/10.1007/978-3-319-75319-5_3\">https://doi.org/10.1007/978-3-319-75319-5_3</a>."},"publication":"Reduced-Order Modeling (ROM) for Simulation and Optimization","user_id":"47427","doi":"10.1007/978-3-319-75319-5_3","_id":"8754","language":[{"iso":"eng"}],"page":"47-72","publication_status":"published","date_updated":"2022-01-06T07:04:00Z","publication_identifier":{"isbn":["9783319753188","9783319753195"]},"author":[{"first_name":"Dennis","last_name":"Beermann","full_name":"Beermann, Dennis"},{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"},{"full_name":"Peitz, Sebastian","last_name":"Peitz","first_name":"Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","id":"47427"},{"first_name":"Stefan","last_name":"Volkwein","full_name":"Volkwein, Stefan"}],"title":"Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition","status":"public","year":"2018"},{"status":"public","user_id":"47427","volume":31,"page":"3359-3380","_id":"8755","project":[{"_id":"52","name":"Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"citation":{"apa":"Klus, S., Gelß, P., Peitz, S., &#38; Schütte, C. (2018). Tensor-based dynamic mode decomposition. <i>Nonlinearity</i>, <i>31</i>(7), 3359–3380. <a href=\"https://doi.org/10.1088/1361-6544/aabc8f\">https://doi.org/10.1088/1361-6544/aabc8f</a>","ieee":"S. Klus, P. Gelß, S. Peitz, and C. Schütte, “Tensor-based dynamic mode decomposition,” <i>Nonlinearity</i>, vol. 31, no. 7, pp. 3359–3380, 2018.","short":"S. Klus, P. Gelß, S. Peitz, C. Schütte, Nonlinearity 31 (2018) 3359–3380.","chicago":"Klus, Stefan, Patrick Gelß, Sebastian Peitz, and Christof Schütte. “Tensor-Based Dynamic Mode Decomposition.” <i>Nonlinearity</i> 31, no. 7 (2018): 3359–80. <a href=\"https://doi.org/10.1088/1361-6544/aabc8f\">https://doi.org/10.1088/1361-6544/aabc8f</a>.","mla":"Klus, Stefan, et al. “Tensor-Based Dynamic Mode Decomposition.” <i>Nonlinearity</i>, vol. 31, no. 7, 2018, pp. 3359–80, doi:<a href=\"https://doi.org/10.1088/1361-6544/aabc8f\">10.1088/1361-6544/aabc8f</a>.","ama":"Klus S, Gelß P, Peitz S, Schütte C. Tensor-based dynamic mode decomposition. <i>Nonlinearity</i>. 2018;31(7):3359-3380. doi:<a href=\"https://doi.org/10.1088/1361-6544/aabc8f\">10.1088/1361-6544/aabc8f</a>","bibtex":"@article{Klus_Gelß_Peitz_Schütte_2018, title={Tensor-based dynamic mode decomposition}, volume={31}, DOI={<a href=\"https://doi.org/10.1088/1361-6544/aabc8f\">10.1088/1361-6544/aabc8f</a>}, number={7}, journal={Nonlinearity}, author={Klus, Stefan and Gelß, Patrick and Peitz, Sebastian and Schütte, Christof}, year={2018}, pages={3359–3380} }"},"publication_status":"published","date_updated":"2022-01-06T07:04:00Z","article_type":"original","intvolume":"        31","year":"2018","title":"Tensor-based dynamic mode decomposition","author":[{"last_name":"Klus","first_name":"Stefan","full_name":"Klus, Stefan"},{"first_name":"Patrick","last_name":"Gelß","full_name":"Gelß, Patrick"},{"orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","first_name":"Sebastian","full_name":"Peitz, Sebastian","id":"47427"},{"last_name":"Schütte","first_name":"Christof","full_name":"Schütte, Christof"}],"publication_identifier":{"issn":["0951-7715","1361-6544"]},"doi":"10.1088/1361-6544/aabc8f","language":[{"iso":"eng"}],"abstract":[{"text":"Dynamic mode decomposition (DMD) is a recently developed tool for the analysis of the behavior of complex dynamical systems. In this paper, we will propose an extension of DMD that exploits low-rank tensor decompositions of potentially high-dimensional data sets to compute the corresponding DMD modes and eigenvalues. The goal is to reduce the computational complexity and also the amount of memory required to store the data in order to mitigate the curse of dimensionality. The efficiency of these tensor-based methods will be illustrated with the aid of several different fluid dynamics problems such as the von Kármán vortex street and the simulation of two merging vortices.","lang":"eng"}],"issue":"7","publication":"Nonlinearity","type":"journal_article","department":[{"_id":"101"}],"date_created":"2019-03-29T13:32:04Z"},{"author":[{"full_name":"Beermann, Dennis","first_name":"Dennis","last_name":"Beermann"},{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"},{"id":"47427","first_name":"Sebastian","last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian"},{"full_name":"Volkwein, Stefan","first_name":"Stefan","last_name":"Volkwein"}],"publication_identifier":{"issn":["1617-7061"]},"title":"POD-based multiobjective optimal control of PDEs with non-smooth objectives","status":"public","year":"2018","publication_status":"published","date_updated":"2022-01-06T07:04:00Z","_id":"8757","language":[{"iso":"eng"}],"page":"51-54","user_id":"47427","doi":"10.1002/pamm.201710015","citation":{"mla":"Beermann, Dennis, et al. “POD-Based Multiobjective Optimal Control of PDEs with Non-Smooth Objectives.” <i>PAMM</i>, 2018, pp. 51–54, doi:<a href=\"https://doi.org/10.1002/pamm.201710015\">10.1002/pamm.201710015</a>.","ama":"Beermann D, Dellnitz M, Peitz S, Volkwein S. POD-based multiobjective optimal control of PDEs with non-smooth objectives. In: <i>PAMM</i>. ; 2018:51-54. doi:<a href=\"https://doi.org/10.1002/pamm.201710015\">10.1002/pamm.201710015</a>","bibtex":"@inproceedings{Beermann_Dellnitz_Peitz_Volkwein_2018, title={POD-based multiobjective optimal control of PDEs with non-smooth objectives}, DOI={<a href=\"https://doi.org/10.1002/pamm.201710015\">10.1002/pamm.201710015</a>}, booktitle={PAMM}, author={Beermann, Dennis and Dellnitz, Michael and Peitz, Sebastian and Volkwein, Stefan}, year={2018}, pages={51–54} }","apa":"Beermann, D., Dellnitz, M., Peitz, S., &#38; Volkwein, S. (2018). POD-based multiobjective optimal control of PDEs with non-smooth objectives. In <i>PAMM</i> (pp. 51–54). <a href=\"https://doi.org/10.1002/pamm.201710015\">https://doi.org/10.1002/pamm.201710015</a>","ieee":"D. Beermann, M. Dellnitz, S. Peitz, and S. Volkwein, “POD-based multiobjective optimal control of PDEs with non-smooth objectives,” in <i>PAMM</i>, 2018, pp. 51–54.","short":"D. Beermann, M. Dellnitz, S. Peitz, S. Volkwein, in: PAMM, 2018, pp. 51–54.","chicago":"Beermann, Dennis, Michael Dellnitz, Sebastian Peitz, and Stefan Volkwein. “POD-Based Multiobjective Optimal Control of PDEs with Non-Smooth Objectives.” In <i>PAMM</i>, 51–54, 2018. <a href=\"https://doi.org/10.1002/pamm.201710015\">https://doi.org/10.1002/pamm.201710015</a>."},"publication":"PAMM","project":[{"name":"Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"abstract":[{"lang":"eng","text":"A framework for set‐oriented multiobjective optimal control of partial differential equations using reduced order modeling has recently been developed [1]. Following concepts from localized reduced bases methods, error estimators for the reduced cost functionals are utilized to construct a library of locally valid reduced order models. This way, a superset of the Pareto set can efficiently be computed while maintaining a prescribed error bound. In this article, this algorithm is applied to a problem with non‐smooth objective functionals. Using an academic example, we show that the extension to non‐smooth problems can be realized in a straightforward manner. We then discuss the implications on the numerical results."}],"date_created":"2019-03-29T13:34:25Z","department":[{"_id":"101"}],"type":"conference"},{"year":"2018","status":"public","title":"Vollständige Charakterisierung von piezoelektrischen Scheiben mit Ringelektroden","author":[{"id":"23082","full_name":"Feldmann, Nadine","last_name":"Feldmann","first_name":"Nadine"},{"full_name":"Jurgelucks, Benjamin","first_name":"Benjamin","last_name":"Jurgelucks"},{"id":"11829","full_name":"Claes, Leander","first_name":"Leander","orcid":"0000-0002-4393-268X","last_name":"Claes"},{"id":"213","full_name":"Henning, Bernd","last_name":"Henning","first_name":"Bernd"}],"date_updated":"2022-01-06T07:03:13Z","_id":"6595","language":[{"iso":"eng"}],"user_id":"11829","citation":{"mla":"Feldmann, Nadine, et al. <i>Vollständige Charakterisierung von Piezoelektrischen Scheiben Mit Ringelektroden</i>. 2018.","bibtex":"@book{Feldmann_Jurgelucks_Claes_Henning_2018, place={Workshop “Messtechnische Anwendungen von Ultraschall”, Drübeck}, title={Vollständige Charakterisierung von piezoelektrischen Scheiben mit Ringelektroden}, author={Feldmann, Nadine and Jurgelucks, Benjamin and Claes, Leander and Henning, Bernd}, year={2018} }","ama":"Feldmann N, Jurgelucks B, Claes L, Henning B. <i>Vollständige Charakterisierung von Piezoelektrischen Scheiben Mit Ringelektroden</i>. Workshop “Messtechnische Anwendungen von Ultraschall”, Drübeck; 2018.","ieee":"N. Feldmann, B. Jurgelucks, L. Claes, and B. Henning, <i>Vollständige Charakterisierung von piezoelektrischen Scheiben mit Ringelektroden</i>. Workshop “Messtechnische Anwendungen von Ultraschall”, Drübeck, 2018.","apa":"Feldmann, N., Jurgelucks, B., Claes, L., &#38; Henning, B. (2018). <i>Vollständige Charakterisierung von piezoelektrischen Scheiben mit Ringelektroden</i>. Workshop “Messtechnische Anwendungen von Ultraschall”, Drübeck.","chicago":"Feldmann, Nadine, Benjamin Jurgelucks, Leander Claes, and Bernd Henning. <i>Vollständige Charakterisierung von Piezoelektrischen Scheiben Mit Ringelektroden</i>. Workshop “Messtechnische Anwendungen von Ultraschall”, Drübeck, 2018.","short":"N. Feldmann, B. Jurgelucks, L. Claes, B. Henning, Vollständige Charakterisierung von Piezoelektrischen Scheiben Mit Ringelektroden, Workshop “Messtechnische Anwendungen von Ultraschall”, Drübeck, 2018."},"project":[{"_id":"90","name":"Ein modellbasiertes Messverfahren zur Charakterisierung der frequenzabhängigen Materialeigenschaften von Piezokeramiken unter Verwendung eines einzelnen Probekörperindividuums"}],"date_created":"2019-01-09T16:14:18Z","place":"Workshop \"Messtechnische Anwendungen von Ultraschall\", Drübeck","type":"misc","department":[{"_id":"49"},{"_id":"104"}]},{"status":"public","title":"Improved Neural Control of Movements Manifests in Expertise-Related Differences in Force Output and Brain Network Dynamics","year":"2018","author":[{"last_name":"Gölz","first_name":"Christian","full_name":"Gölz, Christian"},{"last_name":"Voelcker-Rehage","first_name":"Claudia","full_name":"Voelcker-Rehage, Claudia"},{"full_name":"Mora, Karin","last_name":"Mora","first_name":"Karin"},{"first_name":"Eva-Maria","last_name":"Reuter","full_name":"Reuter, Eva-Maria"},{"first_name":"Ben","last_name":"Godde","full_name":"Godde, Ben"},{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"},{"last_name":"Reinsberger","first_name":"Claus","full_name":"Reinsberger, Claus"},{"full_name":"Vieluf, Solveig","first_name":"Solveig","last_name":"Vieluf"}],"publication_identifier":{"issn":["1664-042X"]},"date_updated":"2022-01-06T06:52:55Z","publication_status":"published","language":[{"iso":"eng"}],"_id":"16713","doi":"10.3389/fphys.2018.01540","user_id":"47427","publication":"Frontiers in Physiology","citation":{"mla":"Gölz, Christian, et al. “Improved Neural Control of Movements Manifests in Expertise-Related Differences in Force Output and Brain Network Dynamics.” <i>Frontiers in Physiology</i>, 2018, doi:<a href=\"https://doi.org/10.3389/fphys.2018.01540\">10.3389/fphys.2018.01540</a>.","bibtex":"@article{Gölz_Voelcker-Rehage_Mora_Reuter_Godde_Dellnitz_Reinsberger_Vieluf_2018, title={Improved Neural Control of Movements Manifests in Expertise-Related Differences in Force Output and Brain Network Dynamics}, DOI={<a href=\"https://doi.org/10.3389/fphys.2018.01540\">10.3389/fphys.2018.01540</a>}, journal={Frontiers in Physiology}, author={Gölz, Christian and Voelcker-Rehage, Claudia and Mora, Karin and Reuter, Eva-Maria and Godde, Ben and Dellnitz, Michael and Reinsberger, Claus and Vieluf, Solveig}, year={2018} }","ama":"Gölz C, Voelcker-Rehage C, Mora K, et al. Improved Neural Control of Movements Manifests in Expertise-Related Differences in Force Output and Brain Network Dynamics. <i>Frontiers in Physiology</i>. 2018. doi:<a href=\"https://doi.org/10.3389/fphys.2018.01540\">10.3389/fphys.2018.01540</a>","ieee":"C. Gölz <i>et al.</i>, “Improved Neural Control of Movements Manifests in Expertise-Related Differences in Force Output and Brain Network Dynamics,” <i>Frontiers in Physiology</i>, 2018.","apa":"Gölz, C., Voelcker-Rehage, C., Mora, K., Reuter, E.-M., Godde, B., Dellnitz, M., … Vieluf, S. (2018). Improved Neural Control of Movements Manifests in Expertise-Related Differences in Force Output and Brain Network Dynamics. <i>Frontiers in Physiology</i>. <a href=\"https://doi.org/10.3389/fphys.2018.01540\">https://doi.org/10.3389/fphys.2018.01540</a>","chicago":"Gölz, Christian, Claudia Voelcker-Rehage, Karin Mora, Eva-Maria Reuter, Ben Godde, Michael Dellnitz, Claus Reinsberger, and Solveig Vieluf. “Improved Neural Control of Movements Manifests in Expertise-Related Differences in Force Output and Brain Network Dynamics.” <i>Frontiers in Physiology</i>, 2018. <a href=\"https://doi.org/10.3389/fphys.2018.01540\">https://doi.org/10.3389/fphys.2018.01540</a>.","short":"C. Gölz, C. Voelcker-Rehage, K. Mora, E.-M. Reuter, B. Godde, M. Dellnitz, C. Reinsberger, S. Vieluf, Frontiers in Physiology (2018)."},"date_created":"2020-04-16T14:08:06Z","type":"journal_article","department":[{"_id":"101"}]},{"title":"Age- and Expertise-Related Differences of Sensorimotor Network Dynamics during Force Control","status":"public","year":"2018","author":[{"last_name":"Vieluf","first_name":"Solveig","full_name":"Vieluf, Solveig"},{"first_name":"Karin","last_name":"Mora","full_name":"Mora, Karin"},{"first_name":"Christian","last_name":"Gölz","full_name":"Gölz, Christian"},{"full_name":"Reuter, Eva-Maria","last_name":"Reuter","first_name":"Eva-Maria"},{"full_name":"Godde, Ben","last_name":"Godde","first_name":"Ben"},{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"},{"last_name":"Reinsberger","first_name":"Claus","full_name":"Reinsberger, Claus"},{"last_name":"Voelcker-Rehage","first_name":"Claudia","full_name":"Voelcker-Rehage, Claudia"}],"publication_identifier":{"issn":["0306-4522"]},"date_updated":"2022-01-06T06:52:55Z","publication_status":"published","page":"203-213","language":[{"iso":"eng"}],"_id":"16714","doi":"10.1016/j.neuroscience.2018.07.025","user_id":"47427","publication":"Neuroscience","citation":{"bibtex":"@article{Vieluf_Mora_Gölz_Reuter_Godde_Dellnitz_Reinsberger_Voelcker-Rehage_2018, title={Age- and Expertise-Related Differences of Sensorimotor Network Dynamics during Force Control}, DOI={<a href=\"https://doi.org/10.1016/j.neuroscience.2018.07.025\">10.1016/j.neuroscience.2018.07.025</a>}, journal={Neuroscience}, author={Vieluf, Solveig and Mora, Karin and Gölz, Christian and Reuter, Eva-Maria and Godde, Ben and Dellnitz, Michael and Reinsberger, Claus and Voelcker-Rehage, Claudia}, year={2018}, pages={203–213} }","ama":"Vieluf S, Mora K, Gölz C, et al. Age- and Expertise-Related Differences of Sensorimotor Network Dynamics during Force Control. <i>Neuroscience</i>. 2018:203-213. doi:<a href=\"https://doi.org/10.1016/j.neuroscience.2018.07.025\">10.1016/j.neuroscience.2018.07.025</a>","mla":"Vieluf, Solveig, et al. “Age- and Expertise-Related Differences of Sensorimotor Network Dynamics during Force Control.” <i>Neuroscience</i>, 2018, pp. 203–13, doi:<a href=\"https://doi.org/10.1016/j.neuroscience.2018.07.025\">10.1016/j.neuroscience.2018.07.025</a>.","short":"S. Vieluf, K. Mora, C. Gölz, E.-M. Reuter, B. Godde, M. Dellnitz, C. Reinsberger, C. Voelcker-Rehage, Neuroscience (2018) 203–213.","chicago":"Vieluf, Solveig, Karin Mora, Christian Gölz, Eva-Maria Reuter, Ben Godde, Michael Dellnitz, Claus Reinsberger, and Claudia Voelcker-Rehage. “Age- and Expertise-Related Differences of Sensorimotor Network Dynamics during Force Control.” <i>Neuroscience</i>, 2018, 203–13. <a href=\"https://doi.org/10.1016/j.neuroscience.2018.07.025\">https://doi.org/10.1016/j.neuroscience.2018.07.025</a>.","ieee":"S. Vieluf <i>et al.</i>, “Age- and Expertise-Related Differences of Sensorimotor Network Dynamics during Force Control,” <i>Neuroscience</i>, pp. 203–213, 2018.","apa":"Vieluf, S., Mora, K., Gölz, C., Reuter, E.-M., Godde, B., Dellnitz, M., … Voelcker-Rehage, C. (2018). Age- and Expertise-Related Differences of Sensorimotor Network Dynamics during Force Control. <i>Neuroscience</i>, 203–213. <a href=\"https://doi.org/10.1016/j.neuroscience.2018.07.025\">https://doi.org/10.1016/j.neuroscience.2018.07.025</a>"},"date_created":"2020-04-16T14:08:51Z","type":"journal_article","department":[{"_id":"101"}]},{"_id":"16715","language":[{"iso":"eng"}],"page":"471-512","volume":28,"user_id":"47427","doi":"10.1007/s00332-017-9415-0","publication_identifier":{"issn":["0938-8974","1432-1467"]},"author":[{"first_name":"Andreas","last_name":"Bittracher","full_name":"Bittracher, Andreas"},{"full_name":"Koltai, Péter","first_name":"Péter","last_name":"Koltai"},{"first_name":"Stefan","last_name":"Klus","full_name":"Klus, Stefan"},{"last_name":"Banisch","first_name":"Ralf","full_name":"Banisch, Ralf"},{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"},{"full_name":"Schütte, Christof","last_name":"Schütte","first_name":"Christof"}],"year":"2018","status":"public","title":"Transition Manifolds of Complex Metastable Systems","intvolume":"        28","publication_status":"published","date_updated":"2022-01-06T06:52:55Z","date_created":"2020-04-16T14:09:31Z","department":[{"_id":"101"}],"type":"journal_article","citation":{"apa":"Bittracher, A., Koltai, P., Klus, S., Banisch, R., Dellnitz, M., &#38; Schütte, C. (2018). Transition Manifolds of Complex Metastable Systems. <i>Journal of Nonlinear Science</i>, <i>28</i>, 471–512. <a href=\"https://doi.org/10.1007/s00332-017-9415-0\">https://doi.org/10.1007/s00332-017-9415-0</a>","mla":"Bittracher, Andreas, et al. “Transition Manifolds of Complex Metastable Systems.” <i>Journal of Nonlinear Science</i>, vol. 28, 2018, pp. 471–512, doi:<a href=\"https://doi.org/10.1007/s00332-017-9415-0\">10.1007/s00332-017-9415-0</a>.","ieee":"A. Bittracher, P. Koltai, S. Klus, R. Banisch, M. Dellnitz, and C. Schütte, “Transition Manifolds of Complex Metastable Systems,” <i>Journal of Nonlinear Science</i>, vol. 28, pp. 471–512, 2018.","chicago":"Bittracher, Andreas, Péter Koltai, Stefan Klus, Ralf Banisch, Michael Dellnitz, and Christof Schütte. “Transition Manifolds of Complex Metastable Systems.” <i>Journal of Nonlinear Science</i> 28 (2018): 471–512. <a href=\"https://doi.org/10.1007/s00332-017-9415-0\">https://doi.org/10.1007/s00332-017-9415-0</a>.","short":"A. Bittracher, P. Koltai, S. Klus, R. Banisch, M. Dellnitz, C. Schütte, Journal of Nonlinear Science 28 (2018) 471–512.","ama":"Bittracher A, Koltai P, Klus S, Banisch R, Dellnitz M, Schütte C. Transition Manifolds of Complex Metastable Systems. <i>Journal of Nonlinear Science</i>. 2018;28:471-512. doi:<a href=\"https://doi.org/10.1007/s00332-017-9415-0\">10.1007/s00332-017-9415-0</a>","bibtex":"@article{Bittracher_Koltai_Klus_Banisch_Dellnitz_Schütte_2018, title={Transition Manifolds of Complex Metastable Systems}, volume={28}, DOI={<a href=\"https://doi.org/10.1007/s00332-017-9415-0\">10.1007/s00332-017-9415-0</a>}, journal={Journal of Nonlinear Science}, author={Bittracher, Andreas and Koltai, Péter and Klus, Stefan and Banisch, Ralf and Dellnitz, Michael and Schütte, Christof}, year={2018}, pages={471–512} }"},"publication":"Journal of Nonlinear Science"},{"type":"preprint","department":[{"_id":"101"}],"oa":"1","date_created":"2020-03-13T12:43:14Z","abstract":[{"text":"In a recent article, we presented a framework to control nonlinear partial\r\ndifferential equations (PDEs) by means of Koopman operator based reduced models\r\nand concepts from switched systems. The main idea was to transform a control\r\nsystem into a set of autonomous systems for which the optimal switching\r\nsequence has to be computed. These individual systems can be approximated very\r\nefficiently by reduced order models obtained from data, and one can guarantee\r\nequality of the full and the reduced objective function under certain\r\nassumptions. In this article, we extend these results to continuous control\r\ninputs using convex combinations of multiple Koopman operators corresponding to\r\nconstant controls, which results in a bilinear control system. Although\r\nequality of the objectives can be carried over when the PDE depends linearly on\r\nthe control, we show that this approach is also valid in other scenarios using\r\nseveral flow control examples of varying complexity.","lang":"eng"}],"publication":"arXiv:1801.06419","citation":{"ama":"Peitz S. Controlling nonlinear PDEs using low-dimensional bilinear approximations  obtained from data. <i>arXiv:180106419</i>. 2018.","bibtex":"@article{Peitz_2018, title={Controlling nonlinear PDEs using low-dimensional bilinear approximations  obtained from data}, journal={arXiv:1801.06419}, author={Peitz, Sebastian}, year={2018} }","mla":"Peitz, Sebastian. “Controlling Nonlinear PDEs Using Low-Dimensional Bilinear Approximations  Obtained from Data.” <i>ArXiv:1801.06419</i>, 2018.","chicago":"Peitz, Sebastian. “Controlling Nonlinear PDEs Using Low-Dimensional Bilinear Approximations  Obtained from Data.” <i>ArXiv:1801.06419</i>, 2018.","short":"S. Peitz, ArXiv:1801.06419 (2018).","apa":"Peitz, S. (2018). Controlling nonlinear PDEs using low-dimensional bilinear approximations  obtained from data. <i>ArXiv:1801.06419</i>.","ieee":"S. Peitz, “Controlling nonlinear PDEs using low-dimensional bilinear approximations  obtained from data,” <i>arXiv:1801.06419</i>. 2018."},"user_id":"47427","main_file_link":[{"url":"https://arxiv.org/pdf/1801.06419.pdf","open_access":"1"}],"language":[{"iso":"eng"}],"_id":"16292","date_updated":"2022-01-06T06:52:48Z","year":"2018","title":"Controlling nonlinear PDEs using low-dimensional bilinear approximations  obtained from data","status":"public","author":[{"id":"47427","full_name":"Peitz, Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","first_name":"Sebastian"}]},{"department":[{"_id":"101"}],"oa":"1","type":"preprint","date_created":"2020-03-13T12:44:12Z","project":[{"name":"Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"abstract":[{"lang":"eng","text":"Kernel transfer operators, which can be regarded as approximations of\r\ntransfer operators such as the Perron-Frobenius or Koopman operator in\r\nreproducing kernel Hilbert spaces, are defined in terms of covariance and\r\ncross-covariance operators and have been shown to be closely related to the\r\nconditional mean embedding framework developed by the machine learning\r\ncommunity. The goal of this paper is to show how the dominant eigenfunctions of\r\nthese operators in combination with gradient-based optimization techniques can\r\nbe used to detect long-lived coherent patterns in high-dimensional time-series\r\ndata. The results will be illustrated using video data and a fluid flow\r\nexample."}],"citation":{"bibtex":"@article{Klus_Peitz_Schuster_2018, title={Analyzing high-dimensional time-series data using kernel transfer  operator eigenfunctions}, journal={arXiv:1805.10118}, author={Klus, Stefan and Peitz, Sebastian and Schuster, Ingmar}, year={2018} }","ama":"Klus S, Peitz S, Schuster I. Analyzing high-dimensional time-series data using kernel transfer  operator eigenfunctions. <i>arXiv:180510118</i>. 2018.","mla":"Klus, Stefan, et al. “Analyzing High-Dimensional Time-Series Data Using Kernel Transfer  Operator Eigenfunctions.” <i>ArXiv:1805.10118</i>, 2018.","chicago":"Klus, Stefan, Sebastian Peitz, and Ingmar Schuster. “Analyzing High-Dimensional Time-Series Data Using Kernel Transfer  Operator Eigenfunctions.” <i>ArXiv:1805.10118</i>, 2018.","short":"S. Klus, S. Peitz, I. Schuster, ArXiv:1805.10118 (2018).","ieee":"S. Klus, S. Peitz, and I. Schuster, “Analyzing high-dimensional time-series data using kernel transfer  operator eigenfunctions,” <i>arXiv:1805.10118</i>. 2018.","apa":"Klus, S., Peitz, S., &#38; Schuster, I. (2018). Analyzing high-dimensional time-series data using kernel transfer  operator eigenfunctions. <i>ArXiv:1805.10118</i>."},"publication":"arXiv:1805.10118","user_id":"47427","_id":"16293","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/1805.10118.pdf"}],"date_updated":"2022-01-06T06:52:48Z","author":[{"last_name":"Klus","first_name":"Stefan","full_name":"Klus, Stefan"},{"id":"47427","full_name":"Peitz, Sebastian","first_name":"Sebastian","last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X"},{"full_name":"Schuster, Ingmar","last_name":"Schuster","first_name":"Ingmar"}],"title":"Analyzing high-dimensional time-series data using kernel transfer  operator eigenfunctions","status":"public","year":"2018"},{"citation":{"ieee":"M. A. Fiol, G. Mazzuoccolo, and E. Steffen, “Measures of Edge-Uncolorability of Cubic Graphs,” <i>The Electronic Journal of Combinatorics</i>, vol. 25, no. 4, 2018.","apa":"Fiol, M. A., Mazzuoccolo, G., &#38; Steffen, E. (2018). Measures of Edge-Uncolorability of Cubic Graphs. <i>The Electronic Journal of Combinatorics</i>, <i>25</i>(4).","mla":"Fiol, M. A., et al. “Measures of Edge-Uncolorability of Cubic Graphs.” <i>The Electronic Journal of Combinatorics</i>, vol. 25, no. 4, P4.54, 2018.","bibtex":"@article{Fiol_Mazzuoccolo_Steffen_2018, title={Measures of Edge-Uncolorability of Cubic Graphs}, volume={25}, number={4P4.54}, journal={The Electronic Journal of Combinatorics}, author={Fiol, M. A. and Mazzuoccolo, Guiseppe and Steffen, Eckhard}, year={2018} }","chicago":"Fiol, M. A., Guiseppe Mazzuoccolo, and Eckhard Steffen. “Measures of Edge-Uncolorability of Cubic Graphs.” <i>The Electronic Journal of Combinatorics</i> 25, no. 4 (2018).","ama":"Fiol MA, Mazzuoccolo G, Steffen E. Measures of Edge-Uncolorability of Cubic Graphs. <i>The Electronic Journal of Combinatorics</i>. 2018;25(4).","short":"M.A. Fiol, G. Mazzuoccolo, E. Steffen, The Electronic Journal of Combinatorics 25 (2018)."},"publication":"The Electronic Journal of Combinatorics","issue":"4","abstract":[{"text":"There are many hard conjectures in graph theory, like Tutte's 5-flow conjecture, and the 5-cycle double cover conjecture, which would be true in general if they would be true for cubic graphs. Since most of them are trivially true for 3-edge-colorable cubic graphs, cubic graphs which are not 3-edge-colorable, often called snarks, play a key role in this context. Here, we survey parameters measuring how far apart a non 3-edge-colorable graph is from being 3-edge-colorable. We study their interrelation and prove some new results. Besides getting new insight into the structure of snarks, we show that such  measures give partial results with respect to these important conjectures. The paper closes with a list of open problems and conjectures.","lang":"eng"}],"date_created":"2019-06-05T09:59:10Z","department":[{"_id":"542"}],"type":"journal_article","keyword":["Cubic graph","Tait coloring","Snark","Boole coloring","Berge's conjecture","Tutte's 5-flow conjecture"],"author":[{"full_name":"Fiol, M. A.","last_name":"Fiol","first_name":"M. A."},{"full_name":"Mazzuoccolo, Guiseppe","last_name":"Mazzuoccolo","first_name":"Guiseppe"},{"first_name":"Eckhard","last_name":"Steffen","full_name":"Steffen, Eckhard","id":"15548"}],"year":"2018","title":"Measures of Edge-Uncolorability of Cubic Graphs","status":"public","article_type":"original","intvolume":"        25","date_updated":"2022-01-06T06:50:30Z","language":[{"iso":"eng"}],"_id":"10129","article_number":"P4.54","volume":25,"user_id":"15540"},{"citation":{"bibtex":"@article{Jin_Mazzuoccolo_Steffen_2018, title={Cores, joins  and the Fano-flow conjectures}, volume={38}, DOI={<a href=\"https://doi.org/10.7151/dmgt.1999\">10.7151/dmgt.1999</a>}, journal={Discussiones Mathematicae Graph Theory}, author={Jin, Ligang and Mazzuoccolo, Giuseppe and Steffen, Eckhard}, year={2018}, pages={165–175} }","ama":"Jin L, Mazzuoccolo G, Steffen E. Cores, joins  and the Fano-flow conjectures. <i>Discussiones Mathematicae Graph Theory</i>. 2018;38:165-175. doi:<a href=\"https://doi.org/10.7151/dmgt.1999\">10.7151/dmgt.1999</a>","mla":"Jin, Ligang, et al. “Cores, Joins  and the Fano-Flow Conjectures.” <i>Discussiones Mathematicae Graph Theory</i>, vol. 38, 2018, pp. 165–75, doi:<a href=\"https://doi.org/10.7151/dmgt.1999\">10.7151/dmgt.1999</a>.","short":"L. Jin, G. Mazzuoccolo, E. Steffen, Discussiones Mathematicae Graph Theory 38 (2018) 165–175.","chicago":"Jin, Ligang, Giuseppe Mazzuoccolo, and Eckhard Steffen. “Cores, Joins  and the Fano-Flow Conjectures.” <i>Discussiones Mathematicae Graph Theory</i> 38 (2018): 165–75. <a href=\"https://doi.org/10.7151/dmgt.1999\">https://doi.org/10.7151/dmgt.1999</a>.","ieee":"L. Jin, G. Mazzuoccolo, and E. Steffen, “Cores, joins  and the Fano-flow conjectures,” <i>Discussiones Mathematicae Graph Theory</i>, vol. 38, pp. 165–175, 2018.","apa":"Jin, L., Mazzuoccolo, G., &#38; Steffen, E. (2018). Cores, joins  and the Fano-flow conjectures. <i>Discussiones Mathematicae Graph Theory</i>, <i>38</i>, 165–175. <a href=\"https://doi.org/10.7151/dmgt.1999\">https://doi.org/10.7151/dmgt.1999</a>"},"publication":"Discussiones Mathematicae Graph Theory","date_created":"2019-06-05T10:08:41Z","department":[{"_id":"542"}],"type":"journal_article","author":[{"last_name":"Jin","first_name":"Ligang","full_name":"Jin, Ligang"},{"last_name":"Mazzuoccolo","first_name":"Giuseppe","full_name":"Mazzuoccolo, Giuseppe"},{"id":"15548","full_name":"Steffen, Eckhard","first_name":"Eckhard","last_name":"Steffen"}],"publication_identifier":{"issn":["1234-3099","2083-5892"]},"year":"2018","title":"Cores, joins  and the Fano-flow conjectures","status":"public","intvolume":"        38","date_updated":"2022-01-06T06:50:30Z","publication_status":"published","language":[{"iso":"eng"}],"_id":"10132","page":"165-175","volume":38,"doi":"10.7151/dmgt.1999","user_id":"15540"},{"citation":{"ieee":"E. Steffen, “Approximating Vizing’s independence number conjecture,” <i>Australasian Journal of Combinatorics</i>, vol. 71, no. 1, pp. 153–160, 2018.","apa":"Steffen, E. (2018). Approximating Vizing’s independence number conjecture. <i>Australasian Journal of Combinatorics</i>, <i>71</i>(1), 153–160.","short":"E. Steffen, Australasian Journal of Combinatorics 71 (2018) 153–160.","chicago":"Steffen, Eckhard. “Approximating Vizing’s Independence Number Conjecture.” <i>Australasian Journal of Combinatorics</i> 71, no. 1 (2018): 153–60.","mla":"Steffen, Eckhard. “Approximating Vizing’s Independence Number Conjecture.” <i>Australasian Journal of Combinatorics</i>, vol. 71, no. 1, 2018, pp. 153–60.","bibtex":"@article{Steffen_2018, title={Approximating Vizing’s independence number conjecture}, volume={71}, number={1}, journal={Australasian Journal of Combinatorics}, author={Steffen, Eckhard}, year={2018}, pages={153–160} }","ama":"Steffen E. Approximating Vizing’s independence number conjecture. <i>Australasian Journal of Combinatorics</i>. 2018;71(1):153-160."},"issue":"1","publication":"Australasian Journal of Combinatorics","date_created":"2019-06-07T08:36:36Z","department":[{"_id":"542"}],"type":"journal_article","author":[{"full_name":"Steffen, Eckhard","first_name":"Eckhard","last_name":"Steffen","id":"15548"}],"year":"2018","status":"public","title":"Approximating Vizing’s independence number conjecture","intvolume":"        71","publication_status":"published","date_updated":"2022-01-06T06:50:31Z","language":[{"iso":"eng"}],"_id":"10142","page":"153-160","volume":71,"user_id":"15540"},{"project":[{"name":"Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"citation":{"short":"S. Peitz, S. Ober-Blöbaum, M. Dellnitz, Acta Applicandae Mathematicae 161 (2018) 171–199.","chicago":"Peitz, Sebastian, Sina Ober-Blöbaum, and Michael Dellnitz. “Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling.” <i>Acta Applicandae Mathematicae</i> 161, no. 1 (2018): 171–199. <a href=\"https://doi.org/10.1007/s10440-018-0209-7\">https://doi.org/10.1007/s10440-018-0209-7</a>.","ieee":"S. Peitz, S. Ober-Blöbaum, and M. Dellnitz, “Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling,” <i>Acta Applicandae Mathematicae</i>, vol. 161, no. 1, pp. 171–199, 2018, doi: <a href=\"https://doi.org/10.1007/s10440-018-0209-7\">10.1007/s10440-018-0209-7</a>.","apa":"Peitz, S., Ober-Blöbaum, S., &#38; Dellnitz, M. (2018). Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling. <i>Acta Applicandae Mathematicae</i>, <i>161</i>(1), 171–199. <a href=\"https://doi.org/10.1007/s10440-018-0209-7\">https://doi.org/10.1007/s10440-018-0209-7</a>","bibtex":"@article{Peitz_Ober-Blöbaum_Dellnitz_2018, title={Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling}, volume={161}, DOI={<a href=\"https://doi.org/10.1007/s10440-018-0209-7\">10.1007/s10440-018-0209-7</a>}, number={1}, journal={Acta Applicandae Mathematicae}, author={Peitz, Sebastian and Ober-Blöbaum, Sina and Dellnitz, Michael}, year={2018}, pages={171–199} }","ama":"Peitz S, Ober-Blöbaum S, Dellnitz M. Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling. <i>Acta Applicandae Mathematicae</i>. 2018;161(1):171–199. doi:<a href=\"https://doi.org/10.1007/s10440-018-0209-7\">10.1007/s10440-018-0209-7</a>","mla":"Peitz, Sebastian, et al. “Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling.” <i>Acta Applicandae Mathematicae</i>, vol. 161, no. 1, 2018, pp. 171–199, doi:<a href=\"https://doi.org/10.1007/s10440-018-0209-7\">10.1007/s10440-018-0209-7</a>."},"volume":161,"user_id":"15694","_id":"8753","page":"171–199","status":"public","department":[{"_id":"101"}],"type":"journal_article","date_created":"2019-03-29T13:30:41Z","abstract":[{"lang":"eng","text":"In a wide range of applications it is desirable to optimally control a dynamical system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a single optimal solution, the set of optimal compromises, the so-called Pareto set, has to be approximated. When the problem under consideration is described by a partial differential equation (PDE), as is the case for fluid flow, the computational cost rapidly increases and makes its direct treatment infeasible. Reduced order modeling is a very popular method to reduce the computational cost, in particular in a multi query context such as uncertainty quantification, parameter estimation or optimization. In this article, we show how to combine reduced order modeling and multiobjective optimal control techniques in order to efficiently solve multiobjective optimal control problems constrained by PDEs. We consider a global, derivative free optimization method as well as a local, gradient-based approach for which the optimality system is derived in two different ways. The methods are compared with regard to the solution quality as well as the computational effort and they are illustrated using the example of the flow around a cylinder and a backward-facing-step channel flow."}],"publication":"Acta Applicandae Mathematicae","issue":"1","doi":"10.1007/s10440-018-0209-7","language":[{"iso":"eng"}],"intvolume":"       161","date_updated":"2022-01-21T10:01:41Z","publication_status":"published","publication_identifier":{"issn":["0167-8019","1572-9036"]},"author":[{"id":"47427","full_name":"Peitz, Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","first_name":"Sebastian"},{"id":"16494","first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina"},{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"}],"year":"2018","title":"Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling"}]