[{"issue":"3","year":"2023","page":"709-741","intvolume":" 85","citation":{"ama":"Gebken B, Bieker K, Peitz S. On the structure of regularization paths for piecewise differentiable regularization terms. Journal of Global Optimization. 2023;85(3):709-741. doi:10.1007/s10898-022-01223-2","chicago":"Gebken, Bennet, Katharina Bieker, and Sebastian Peitz. “On the Structure of Regularization Paths for Piecewise Differentiable Regularization Terms.” Journal of Global Optimization 85, no. 3 (2023): 709–41. https://doi.org/10.1007/s10898-022-01223-2.","ieee":"B. Gebken, K. Bieker, and S. Peitz, “On the structure of regularization paths for piecewise differentiable regularization terms,” Journal of Global Optimization, vol. 85, no. 3, pp. 709–741, 2023, doi: 10.1007/s10898-022-01223-2.","apa":"Gebken, B., Bieker, K., & Peitz, S. (2023). On the structure of regularization paths for piecewise differentiable regularization terms. Journal of Global Optimization, 85(3), 709–741. https://doi.org/10.1007/s10898-022-01223-2","mla":"Gebken, Bennet, et al. “On the Structure of Regularization Paths for Piecewise Differentiable Regularization Terms.” Journal of Global Optimization, vol. 85, no. 3, 2023, pp. 709–41, doi:10.1007/s10898-022-01223-2.","bibtex":"@article{Gebken_Bieker_Peitz_2023, title={On the structure of regularization paths for piecewise differentiable regularization terms}, volume={85}, DOI={10.1007/s10898-022-01223-2}, number={3}, journal={Journal of Global Optimization}, author={Gebken, Bennet and Bieker, Katharina and Peitz, Sebastian}, year={2023}, pages={709–741} }","short":"B. Gebken, K. Bieker, S. Peitz, Journal of Global Optimization 85 (2023) 709–741."},"oa":"1","date_updated":"2023-03-11T17:16:33Z","volume":85,"date_created":"2021-11-15T09:24:59Z","author":[{"id":"32643","full_name":"Gebken, Bennet","last_name":"Gebken","first_name":"Bennet"},{"id":"32829","full_name":"Bieker, Katharina","last_name":"Bieker","first_name":"Katharina"},{"first_name":"Sebastian","orcid":"0000-0002-3389-793X","last_name":"Peitz","full_name":"Peitz, Sebastian","id":"47427"}],"title":"On the structure of regularization paths for piecewise differentiable regularization terms","doi":"10.1007/s10898-022-01223-2","main_file_link":[{"url":"https://link.springer.com/content/pdf/10.1007/s10898-022-01223-2.pdf","open_access":"1"}],"publication":"Journal of Global Optimization","type":"journal_article","abstract":[{"lang":"eng","text":"Regularization is used in many different areas of optimization when solutions\r\nare sought which not only minimize a given function, but also possess a certain\r\ndegree of regularity. Popular applications are image denoising, sparse\r\nregression and machine learning. Since the choice of the regularization\r\nparameter is crucial but often difficult, path-following methods are used to\r\napproximate the entire regularization path, i.e., the set of all possible\r\nsolutions for all regularization parameters. Due to their nature, the\r\ndevelopment of these methods requires structural results about the\r\nregularization path. The goal of this article is to derive these results for\r\nthe case of a smooth objective function which is penalized by a piecewise\r\ndifferentiable regularization term. We do this by treating regularization as a\r\nmultiobjective optimization problem. Our results suggest that even in this\r\ngeneral case, the regularization path is piecewise smooth. Moreover, our theory\r\nallows for a classification of the nonsmooth features that occur in between\r\nsmooth parts. This is demonstrated in two applications, namely support-vector\r\nmachines and exact penalty methods."}],"status":"public","_id":"27426","department":[{"_id":"101"},{"_id":"655"}],"user_id":"47427","language":[{"iso":"eng"}]},{"publication":"IFAC-PapersOnLine","abstract":[{"text":"We present an approach for guaranteed constraint satisfaction by means of data-based optimal control, where the model is unknown and has to be obtained from measurement data. To this end, we utilize the Koopman framework and an eDMD-based bilinear surrogate modeling approach for control systems to show an error bound on predicted observables, i.e., functions of the state. This result is then applied to the constraints of the optimal control problem to show that satisfaction of tightened constraints in the purely data-based surrogate model implies constraint satisfaction for the original system.","lang":"eng"}],"external_id":{"arxiv":["2202.09084"]},"language":[{"iso":"eng"}],"issue":"1","year":"2023","date_created":"2022-02-25T17:14:58Z","title":"Towards reliable data-based optimal and predictive control using extended DMD","type":"conference","status":"public","department":[{"_id":"655"}],"user_id":"47427","_id":"30125","publication_status":"published","page":"169-174","intvolume":" 56","citation":{"chicago":"Schaller, Manuel, Karl Worthmann, Friedrich Philipp, Sebastian Peitz, and Feliks Nüske. “Towards Reliable Data-Based Optimal and Predictive Control Using Extended DMD.” In IFAC-PapersOnLine, 56:169–74, 2023. https://doi.org/10.1016/j.ifacol.2023.02.029.","ieee":"M. Schaller, K. Worthmann, F. Philipp, S. Peitz, and F. Nüske, “Towards reliable data-based optimal and predictive control using extended DMD,” in IFAC-PapersOnLine, 2023, vol. 56, no. 1, pp. 169–174, doi: 10.1016/j.ifacol.2023.02.029.","ama":"Schaller M, Worthmann K, Philipp F, Peitz S, Nüske F. Towards reliable data-based optimal and predictive control using extended DMD. In: IFAC-PapersOnLine. Vol 56. ; 2023:169-174. doi:10.1016/j.ifacol.2023.02.029","mla":"Schaller, Manuel, et al. “Towards Reliable Data-Based Optimal and Predictive Control Using Extended DMD.” IFAC-PapersOnLine, vol. 56, no. 1, 2023, pp. 169–74, doi:10.1016/j.ifacol.2023.02.029.","bibtex":"@inproceedings{Schaller_Worthmann_Philipp_Peitz_Nüske_2023, title={Towards reliable data-based optimal and predictive control using extended DMD}, volume={56}, DOI={10.1016/j.ifacol.2023.02.029}, number={1}, booktitle={IFAC-PapersOnLine}, author={Schaller, Manuel and Worthmann, Karl and Philipp, Friedrich and Peitz, Sebastian and Nüske, Feliks}, year={2023}, pages={169–174} }","short":"M. Schaller, K. Worthmann, F. Philipp, S. Peitz, F. Nüske, in: IFAC-PapersOnLine, 2023, pp. 169–174.","apa":"Schaller, M., Worthmann, K., Philipp, F., Peitz, S., & Nüske, F. (2023). Towards reliable data-based optimal and predictive control using extended DMD. IFAC-PapersOnLine, 56(1), 169–174. https://doi.org/10.1016/j.ifacol.2023.02.029"},"volume":56,"author":[{"full_name":"Schaller, Manuel","last_name":"Schaller","first_name":"Manuel"},{"full_name":"Worthmann, Karl","last_name":"Worthmann","first_name":"Karl"},{"first_name":"Friedrich","full_name":"Philipp, Friedrich","last_name":"Philipp"},{"last_name":"Peitz","orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian","id":"47427","first_name":"Sebastian"},{"first_name":"Feliks","orcid":"0000-0003-2444-7889","last_name":"Nüske","id":"81513","full_name":"Nüske, Feliks"}],"oa":"1","date_updated":"2023-03-17T15:55:33Z","conference":{"name":"12th IFAC Symposium on Nonlinear Control Systems (NOLCOS)"},"doi":"10.1016/j.ifacol.2023.02.029","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S2405896323002173/pdf?md5=164ee9a0343a1bd0e0b9ac4187e44b77&pid=1-s2.0-S2405896323002173-main.pdf","open_access":"1"}]},{"user_id":"47427","department":[{"_id":"655"}],"_id":"46579","external_id":{"arxiv":["2307.15325"]},"language":[{"iso":"eng"}],"type":"preprint","publication":"arXiv:2307.15325","status":"public","abstract":[{"text":"The Koopman operator has become an essential tool for data-driven analysis, prediction and control of complex systems, the main reason being the enormous potential of identifying linear function space representations of nonlinear\r\ndynamics from measurements. Until now, the situation where for large-scale systems, we (i) only have access to partial observations (i.e., measurements, as is very common for experimental data) or (ii) deliberately perform coarse\r\ngraining (for efficiency reasons) has not been treated to its full extent. In this paper, we address the pitfall associated with this situation, that the classical EDMD algorithm does not automatically provide a Koopman operator approximation for the underlying system if we do not carefully select the number of observables. Moreover, we show that symmetries in the system dynamics can be carried over to the Koopman operator, which allows us to massively increase the model efficiency. We also briefly draw a connection to domain decomposition techniques for partial differential equations and present numerical evidence using the Kuramoto--Sivashinsky equation.","lang":"eng"}],"date_created":"2023-08-21T05:52:24Z","author":[{"first_name":"Sebastian","id":"47427","full_name":"Peitz, Sebastian","last_name":"Peitz","orcid":"0000-0002-3389-793X"},{"first_name":"Hans","id":"98879","full_name":"Harder, Hans","last_name":"Harder"},{"full_name":"Nüske, Feliks","last_name":"Nüske","first_name":"Feliks"},{"last_name":"Philipp","full_name":"Philipp, Friedrich","first_name":"Friedrich"},{"full_name":"Schaller, Manuel","last_name":"Schaller","first_name":"Manuel"},{"last_name":"Worthmann","full_name":"Worthmann, Karl","first_name":"Karl"}],"oa":"1","date_updated":"2023-08-21T05:53:35Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/2307.15325"}],"title":"Partial observations, coarse graining and equivariance in Koopman operator theory for large-scale dynamical systems","citation":{"short":"S. Peitz, H. Harder, F. Nüske, F. Philipp, M. Schaller, K. Worthmann, ArXiv:2307.15325 (2023).","mla":"Peitz, Sebastian, et al. “Partial Observations, Coarse Graining and Equivariance in Koopman Operator Theory for Large-Scale Dynamical Systems.” ArXiv:2307.15325, 2023.","bibtex":"@article{Peitz_Harder_Nüske_Philipp_Schaller_Worthmann_2023, title={Partial observations, coarse graining and equivariance in Koopman operator theory for large-scale dynamical systems}, journal={arXiv:2307.15325}, author={Peitz, Sebastian and Harder, Hans and Nüske, Feliks and Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl}, year={2023} }","apa":"Peitz, S., Harder, H., Nüske, F., Philipp, F., Schaller, M., & Worthmann, K. (2023). Partial observations, coarse graining and equivariance in Koopman operator theory for large-scale dynamical systems. In arXiv:2307.15325.","chicago":"Peitz, Sebastian, Hans Harder, Feliks Nüske, Friedrich Philipp, Manuel Schaller, and Karl Worthmann. “Partial Observations, Coarse Graining and Equivariance in Koopman Operator Theory for Large-Scale Dynamical Systems.” ArXiv:2307.15325, 2023.","ieee":"S. Peitz, H. Harder, F. Nüske, F. Philipp, M. Schaller, and K. Worthmann, “Partial observations, coarse graining and equivariance in Koopman operator theory for large-scale dynamical systems,” arXiv:2307.15325. 2023.","ama":"Peitz S, Harder H, Nüske F, Philipp F, Schaller M, Worthmann K. Partial observations, coarse graining and equivariance in Koopman operator theory for large-scale dynamical systems. arXiv:230715325. Published online 2023."},"year":"2023"},{"publication":"Journal of Nonlinear Science","type":"journal_article","status":"public","abstract":[{"lang":"eng","text":"The Koopman operator has become an essential tool for data-driven approximation of dynamical (control) systems in recent years, e.g., via extended dynamic mode decomposition. Despite its popularity, convergence results and, in particular, error bounds are still quite scarce. In this paper, we derive probabilistic bounds for the approximation error and the prediction error depending on the number of training data points; for both ordinary and stochastic differential equations. Moreover, we extend our analysis to nonlinear control-affine systems using either ergodic trajectories or i.i.d.\r\nsamples. Here, we exploit the linearity of the Koopman generator to obtain a bilinear system and, thus, circumvent the curse of dimensionality since we do not autonomize the system by augmenting the state by the control inputs. To the\r\nbest of our knowledge, this is the first finite-data error analysis in the stochastic and/or control setting. Finally, we demonstrate the effectiveness of the proposed approach by comparing it with state-of-the-art techniques showing its superiority whenever state and control are coupled."}],"department":[{"_id":"101"},{"_id":"655"}],"user_id":"47427","_id":"23428","language":[{"iso":"eng"}],"article_number":"14","publication_status":"published","intvolume":" 33","citation":{"ama":"Nüske F, Peitz S, Philipp F, Schaller M, Worthmann K. Finite-data error bounds for Koopman-based prediction and control. Journal of Nonlinear Science. 2023;33. doi:10.1007/s00332-022-09862-1","ieee":"F. Nüske, S. Peitz, F. Philipp, M. Schaller, and K. Worthmann, “Finite-data error bounds for Koopman-based prediction and control,” Journal of Nonlinear Science, vol. 33, Art. no. 14, 2023, doi: 10.1007/s00332-022-09862-1.","chicago":"Nüske, Feliks, Sebastian Peitz, Friedrich Philipp, Manuel Schaller, and Karl Worthmann. “Finite-Data Error Bounds for Koopman-Based Prediction and Control.” Journal of Nonlinear Science 33 (2023). https://doi.org/10.1007/s00332-022-09862-1.","short":"F. Nüske, S. Peitz, F. Philipp, M. Schaller, K. Worthmann, Journal of Nonlinear Science 33 (2023).","bibtex":"@article{Nüske_Peitz_Philipp_Schaller_Worthmann_2023, title={Finite-data error bounds for Koopman-based prediction and control}, volume={33}, DOI={10.1007/s00332-022-09862-1}, number={14}, journal={Journal of Nonlinear Science}, author={Nüske, Feliks and Peitz, Sebastian and Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl}, year={2023} }","mla":"Nüske, Feliks, et al. “Finite-Data Error Bounds for Koopman-Based Prediction and Control.” Journal of Nonlinear Science, vol. 33, 14, 2023, doi:10.1007/s00332-022-09862-1.","apa":"Nüske, F., Peitz, S., Philipp, F., Schaller, M., & Worthmann, K. (2023). Finite-data error bounds for Koopman-based prediction and control. Journal of Nonlinear Science, 33, Article 14. https://doi.org/10.1007/s00332-022-09862-1"},"year":"2023","volume":33,"author":[{"id":"81513","full_name":"Nüske, Feliks","last_name":"Nüske","orcid":"0000-0003-2444-7889","first_name":"Feliks"},{"first_name":"Sebastian","orcid":"0000-0002-3389-793X","last_name":"Peitz","id":"47427","full_name":"Peitz, Sebastian"},{"full_name":"Philipp, Friedrich","last_name":"Philipp","first_name":"Friedrich"},{"first_name":"Manuel","full_name":"Schaller, Manuel","last_name":"Schaller"},{"full_name":"Worthmann, Karl","last_name":"Worthmann","first_name":"Karl"}],"date_created":"2021-08-17T12:25:09Z","date_updated":"2023-08-24T07:50:12Z","oa":"1","doi":"10.1007/s00332-022-09862-1","main_file_link":[{"open_access":"1","url":"https://link.springer.com/content/pdf/10.1007/s00332-022-09862-1.pdf"}],"title":"Finite-data error bounds for Koopman-based prediction and control"},{"date_created":"2021-04-09T07:59:19Z","title":"Efficient time stepping for numerical integration using reinforcement learning","issue":"2","year":"2023","external_id":{"arxiv":["arXiv:2104.03562"]},"ddc":["510"],"language":[{"iso":"eng"}],"publication":"SIAM Journal on Scientific Computing","abstract":[{"text":"Many problems in science and engineering require an efficient numerical approximation of integrals or solutions to differential equations. For systems with rapidly changing dynamics, an equidistant discretization is often inadvisable as it results in prohibitively large errors or computational effort. To this end, adaptive schemes, such as solvers based on Runge–Kutta pairs, have been developed which adapt the step size based on local error estimations at each step. While the classical schemes apply very generally and are highly efficient on regular systems, they can behave suboptimally when an inefficient step rejection mechanism is triggered by structurally complex systems such as chaotic systems. To overcome these issues, we propose a method to tailor numerical schemes to the problem class at hand. This is achieved by combining simple, classical quadrature rules or ODE solvers with data-driven time-stepping controllers. Compared with learning solution operators to ODEs directly, it generalizes better to unseen initial data as our approach employs classical numerical schemes as base methods. At the same time it can make use of identified structures of a problem class and, therefore, outperforms state-of-the-art adaptive schemes. Several examples demonstrate superior efficiency. Source code is available at https://github.com/lueckem/quadrature-ML.","lang":"eng"}],"date_updated":"2023-08-25T09:24:50Z","author":[{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"id":"48129","full_name":"Hüllermeier, Eyke","last_name":"Hüllermeier","first_name":"Eyke"},{"first_name":"Marvin","last_name":"Lücke","full_name":"Lücke, Marvin"},{"first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina"},{"last_name":"Offen","orcid":"0000-0002-5940-8057","id":"85279","full_name":"Offen, Christian","first_name":"Christian"},{"first_name":"Sebastian","id":"47427","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","last_name":"Peitz"},{"first_name":"Karlson","orcid":"0000-0001-9407-7903","last_name":"Pfannschmidt","full_name":"Pfannschmidt, Karlson","id":"13472"}],"volume":45,"main_file_link":[{"url":"https://epubs.siam.org/doi/reader/10.1137/21M1412682"}],"doi":"10.1137/21M1412682","publication_status":"published","has_accepted_license":"1","related_material":{"link":[{"url":"https://github.com/lueckem/quadrature-ML","description":"GitHub","relation":"software"}]},"citation":{"short":"M. Dellnitz, E. Hüllermeier, M. Lücke, S. Ober-Blöbaum, C. Offen, S. Peitz, K. Pfannschmidt, SIAM Journal on Scientific Computing 45 (2023) A579–A595.","bibtex":"@article{Dellnitz_Hüllermeier_Lücke_Ober-Blöbaum_Offen_Peitz_Pfannschmidt_2023, title={Efficient time stepping for numerical integration using reinforcement learning}, volume={45}, DOI={10.1137/21M1412682}, number={2}, journal={SIAM Journal on Scientific Computing}, author={Dellnitz, Michael and Hüllermeier, Eyke and Lücke, Marvin and Ober-Blöbaum, Sina and Offen, Christian and Peitz, Sebastian and Pfannschmidt, Karlson}, year={2023}, pages={A579–A595} }","mla":"Dellnitz, Michael, et al. “Efficient Time Stepping for Numerical Integration Using Reinforcement Learning.” SIAM Journal on Scientific Computing, vol. 45, no. 2, 2023, pp. A579–95, doi:10.1137/21M1412682.","apa":"Dellnitz, M., Hüllermeier, E., Lücke, M., Ober-Blöbaum, S., Offen, C., Peitz, S., & Pfannschmidt, K. (2023). Efficient time stepping for numerical integration using reinforcement learning. SIAM Journal on Scientific Computing, 45(2), A579–A595. https://doi.org/10.1137/21M1412682","ieee":"M. Dellnitz et al., “Efficient time stepping for numerical integration using reinforcement learning,” SIAM Journal on Scientific Computing, vol. 45, no. 2, pp. A579–A595, 2023, doi: 10.1137/21M1412682.","chicago":"Dellnitz, Michael, Eyke Hüllermeier, Marvin Lücke, Sina Ober-Blöbaum, Christian Offen, Sebastian Peitz, and Karlson Pfannschmidt. “Efficient Time Stepping for Numerical Integration Using Reinforcement Learning.” SIAM Journal on Scientific Computing 45, no. 2 (2023): A579–95. https://doi.org/10.1137/21M1412682.","ama":"Dellnitz M, Hüllermeier E, Lücke M, et al. Efficient time stepping for numerical integration using reinforcement learning. SIAM Journal on Scientific Computing. 2023;45(2):A579-A595. doi:10.1137/21M1412682"},"page":"A579-A595","intvolume":" 45","_id":"21600","user_id":"47427","department":[{"_id":"101"},{"_id":"636"},{"_id":"355"},{"_id":"655"}],"type":"journal_article","status":"public"},{"intvolume":" 8","citation":{"ieee":"O. Wallscheid et al., “ElectricGrid.jl - A Julia-based modeling and simulationtool for power electronics-driven electric energy grids,” Journal of Open Source Software, vol. 8, no. 89, Art. no. 5616, 2023, doi: 10.21105/joss.05616.","chicago":"Wallscheid, Oliver, Sebastian Peitz, Jan Stenner, Daniel Weber, Septimus Boshoff, Marvin Meyer, Vikas Chidananda, and Oliver Schweins. “ElectricGrid.Jl - A Julia-Based Modeling and Simulationtool for Power Electronics-Driven Electric Energy Grids.” Journal of Open Source Software 8, no. 89 (2023). https://doi.org/10.21105/joss.05616.","ama":"Wallscheid O, Peitz S, Stenner J, et al. ElectricGrid.jl - A Julia-based modeling and simulationtool for power electronics-driven electric energy grids. Journal of Open Source Software. 2023;8(89). doi:10.21105/joss.05616","mla":"Wallscheid, Oliver, et al. “ElectricGrid.Jl - A Julia-Based Modeling and Simulationtool for Power Electronics-Driven Electric Energy Grids.” Journal of Open Source Software, vol. 8, no. 89, 5616, The Open Journal, 2023, doi:10.21105/joss.05616.","short":"O. Wallscheid, S. Peitz, J. Stenner, D. Weber, S. Boshoff, M. Meyer, V. Chidananda, O. Schweins, Journal of Open Source Software 8 (2023).","bibtex":"@article{Wallscheid_Peitz_Stenner_Weber_Boshoff_Meyer_Chidananda_Schweins_2023, title={ElectricGrid.jl - A Julia-based modeling and simulationtool for power electronics-driven electric energy grids}, volume={8}, DOI={10.21105/joss.05616}, number={895616}, journal={Journal of Open Source Software}, publisher={The Open Journal}, author={Wallscheid, Oliver and Peitz, Sebastian and Stenner, Jan and Weber, Daniel and Boshoff, Septimus and Meyer, Marvin and Chidananda, Vikas and Schweins, Oliver}, year={2023} }","apa":"Wallscheid, O., Peitz, S., Stenner, J., Weber, D., Boshoff, S., Meyer, M., Chidananda, V., & Schweins, O. (2023). ElectricGrid.jl - A Julia-based modeling and simulationtool for power electronics-driven electric energy grids. Journal of Open Source Software, 8(89), Article 5616. https://doi.org/10.21105/joss.05616"},"publication_identifier":{"issn":["2475-9066"]},"publication_status":"published","doi":"10.21105/joss.05616","main_file_link":[{"url":"https://joss.theoj.org/papers/10.21105/joss.05616","open_access":"1"}],"volume":8,"author":[{"first_name":"Oliver","id":"11291","full_name":"Wallscheid, Oliver","orcid":"https://orcid.org/0000-0001-9362-8777","last_name":"Wallscheid"},{"full_name":"Peitz, Sebastian","id":"47427","last_name":"Peitz","orcid":"0000-0002-3389-793X","first_name":"Sebastian"},{"first_name":"Jan","last_name":"Stenner","full_name":"Stenner, Jan","id":"65520"},{"orcid":"0000-0003-3367-5998","last_name":"Weber","id":"24041","full_name":"Weber, Daniel","first_name":"Daniel"},{"full_name":"Boshoff, Septimus","last_name":"Boshoff","first_name":"Septimus"},{"full_name":"Meyer, Marvin","last_name":"Meyer","first_name":"Marvin"},{"full_name":"Chidananda, Vikas","last_name":"Chidananda","first_name":"Vikas"},{"first_name":"Oliver","last_name":"Schweins","full_name":"Schweins, Oliver"}],"date_updated":"2023-09-04T11:06:06Z","oa":"1","status":"public","type":"journal_article","article_number":"5616","department":[{"_id":"655"},{"_id":"52"}],"user_id":"47427","_id":"46784","year":"2023","issue":"89","title":"ElectricGrid.jl - A Julia-based modeling and simulationtool for power electronics-driven electric energy grids","date_created":"2023-09-04T11:05:03Z","publisher":"The Open Journal","publication":"Journal of Open Source Software","language":[{"iso":"eng"}],"keyword":["General Earth and Planetary Sciences","General Environmental Science"]},{"citation":{"mla":"Wohlleben, Meike Claudia, et al. “Transferability of a Discrepancy Model for the Dynamics of Electromagnetic Oscillating Circuits.” Proceedings in Applied Mathematics and Mechanics, Wiley, 2023, doi:10.1002/pamm.202300039.","short":"M.C. Wohlleben, L. Muth, S. Peitz, W. Sextro, in: Proceedings in Applied Mathematics and Mechanics, Wiley, 2023.","bibtex":"@inproceedings{Wohlleben_Muth_Peitz_Sextro_2023, title={Transferability of a discrepancy model for the dynamics of electromagnetic oscillating circuits}, DOI={10.1002/pamm.202300039}, booktitle={Proceedings in Applied Mathematics and Mechanics}, publisher={Wiley}, author={Wohlleben, Meike Claudia and Muth, Lars and Peitz, Sebastian and Sextro, Walter}, year={2023} }","apa":"Wohlleben, M. C., Muth, L., Peitz, S., & Sextro, W. (2023). Transferability of a discrepancy model for the dynamics of electromagnetic oscillating circuits. Proceedings in Applied Mathematics and Mechanics. https://doi.org/10.1002/pamm.202300039","ieee":"M. C. Wohlleben, L. Muth, S. Peitz, and W. Sextro, “Transferability of a discrepancy model for the dynamics of electromagnetic oscillating circuits,” 2023, doi: 10.1002/pamm.202300039.","chicago":"Wohlleben, Meike Claudia, Lars Muth, Sebastian Peitz, and Walter Sextro. “Transferability of a Discrepancy Model for the Dynamics of Electromagnetic Oscillating Circuits.” In Proceedings in Applied Mathematics and Mechanics. Wiley, 2023. https://doi.org/10.1002/pamm.202300039.","ama":"Wohlleben MC, Muth L, Peitz S, Sextro W. Transferability of a discrepancy model for the dynamics of electromagnetic oscillating circuits. In: Proceedings in Applied Mathematics and Mechanics. Wiley; 2023. doi:10.1002/pamm.202300039"},"year":"2023","publication_status":"published","quality_controlled":"1","publication_identifier":{"issn":["1617-7061","1617-7061"]},"main_file_link":[{"url":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/pamm.202300039","open_access":"1"}],"doi":"10.1002/pamm.202300039","title":"Transferability of a discrepancy model for the dynamics of electromagnetic oscillating circuits","date_created":"2023-09-06T05:18:05Z","author":[{"first_name":"Meike Claudia","orcid":"0009-0009-9767-7168","last_name":"Wohlleben","id":"43991","full_name":"Wohlleben, Meike Claudia"},{"id":"77313","full_name":"Muth, Lars","orcid":"0000-0002-2938-5616","last_name":"Muth","first_name":"Lars"},{"first_name":"Sebastian","id":"47427","full_name":"Peitz, Sebastian","last_name":"Peitz","orcid":"0000-0002-3389-793X"},{"first_name":"Walter","last_name":"Sextro","id":"21220","full_name":"Sextro, Walter"}],"date_updated":"2023-09-21T14:47:20Z","publisher":"Wiley","oa":"1","status":"public","abstract":[{"text":"Modelling of dynamic systems plays an important role in many engineering disciplines. Two different approaches are physical modelling and data‐driven modelling, both of which have their respective advantages and disadvantages. By combining these two approaches, hybrid models can be created in which the respective disadvantages are mitigated, with discrepancy models being a particular subclass. Here, the basic system behaviour is described physically, that is, in the form of differential equations. Inaccuracies resulting from insufficient modelling or numerics lead to a discrepancy between the measurements and the model, which can be compensated by a data‐driven error correction term. Since discrepancy methods still require a large amount of measurement data, this paper investigates the extent to which a single discrepancy model can be trained for a physical model with additional parameter dependencies without the need for retraining. As an example, a damped electromagnetic oscillating circuit is used. The physical model is realised by a differential equation describing the electric current, considering only inductance and capacitance; dissipation due to resistance is neglected. This creates a discrepancy between measurement and model, which is corrected by a data‐driven model. In the experiments, the inductance and the capacity are varied. It is found that the same data‐driven model can only be used if additional parametric dependencies in the data‐driven term are considered as well.","lang":"eng"}],"type":"conference","publication":"Proceedings in Applied Mathematics and Mechanics","language":[{"iso":"eng"}],"keyword":["Electrical and Electronic Engineering","Atomic and Molecular Physics","and Optics"],"user_id":"77313","department":[{"_id":"655"},{"_id":"151"}],"_id":"46813"},{"publication":"Non-Smooth and Complementarity-Based Distributed Parameter Systems","type":"book_chapter","status":"public","editor":[{"full_name":"Michael, Hintermüller","last_name":"Michael","first_name":"Hintermüller"},{"first_name":"Herzog","last_name":"Roland","full_name":"Roland, Herzog"},{"first_name":"Kanzow","last_name":"Christian","full_name":"Christian, Kanzow"},{"full_name":"Michael, Ulbrich","last_name":"Michael","first_name":"Ulbrich"},{"first_name":"Ulbrich","last_name":"Stefan","full_name":"Stefan, Ulbrich"}],"abstract":[{"lang":"eng","text":"Multiobjective optimization plays an increasingly important role in modern\r\napplications, where several objectives are often of equal importance. The task\r\nin multiobjective optimization and multiobjective optimal control is therefore\r\nto compute the set of optimal compromises (the Pareto set) between the\r\nconflicting objectives. Since the Pareto set generally consists of an infinite\r\nnumber of solutions, the computational effort can quickly become challenging\r\nwhich is particularly problematic when the objectives are costly to evaluate as\r\nis the case for models governed by partial differential equations (PDEs). To\r\ndecrease the numerical effort to an affordable amount, surrogate models can be\r\nused to replace the expensive PDE evaluations. Existing multiobjective\r\noptimization methods using model reduction are limited either to low parameter\r\ndimensions or to few (ideally two) objectives. In this article, we present a\r\ncombination of the reduced basis model reduction method with a continuation\r\napproach using inexact gradients. The resulting approach can handle an\r\narbitrary number of objectives while yielding a significant reduction in\r\ncomputing time."}],"department":[{"_id":"101"},{"_id":"655"}],"user_id":"47427","_id":"16296","language":[{"iso":"eng"}],"publication_identifier":{"isbn":["978-3-030-79392-0"]},"page":"43-76","citation":{"mla":"Banholzer, Stefan, et al. “ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation.” Non-Smooth and Complementarity-Based Distributed Parameter Systems, edited by Hintermüller Michael et al., Springer, 2022, pp. 43–76, doi:10.1007/978-3-030-79393-7_3.","bibtex":"@inbook{Banholzer_Gebken_Dellnitz_Peitz_Volkwein_2022, place={Cham}, title={ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation}, DOI={10.1007/978-3-030-79393-7_3}, booktitle={Non-Smooth and Complementarity-Based Distributed Parameter Systems}, publisher={Springer}, author={Banholzer, Stefan and Gebken, Bennet and Dellnitz, Michael and Peitz, Sebastian and Volkwein, Stefan}, editor={Michael, Hintermüller and Roland, Herzog and Christian, Kanzow and Michael, Ulbrich and Stefan, Ulbrich}, year={2022}, pages={43–76} }","short":"S. Banholzer, B. Gebken, M. Dellnitz, S. Peitz, S. Volkwein, in: H. Michael, H. Roland, K. Christian, U. Michael, U. Stefan (Eds.), Non-Smooth and Complementarity-Based Distributed Parameter Systems, Springer, Cham, 2022, pp. 43–76.","apa":"Banholzer, S., Gebken, B., Dellnitz, M., Peitz, S., & Volkwein, S. (2022). ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation. In H. Michael, H. Roland, K. Christian, U. Michael, & U. Stefan (Eds.), Non-Smooth and Complementarity-Based Distributed Parameter Systems (pp. 43–76). Springer. https://doi.org/10.1007/978-3-030-79393-7_3","ama":"Banholzer S, Gebken B, Dellnitz M, Peitz S, Volkwein S. ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation. In: Michael H, Roland H, Christian K, Michael U, Stefan U, eds. Non-Smooth and Complementarity-Based Distributed Parameter Systems. Springer; 2022:43-76. doi:10.1007/978-3-030-79393-7_3","ieee":"S. Banholzer, B. Gebken, M. Dellnitz, S. Peitz, and S. Volkwein, “ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation,” in Non-Smooth and Complementarity-Based Distributed Parameter Systems, H. Michael, H. Roland, K. Christian, U. Michael, and U. Stefan, Eds. Cham: Springer, 2022, pp. 43–76.","chicago":"Banholzer, Stefan, Bennet Gebken, Michael Dellnitz, Sebastian Peitz, and Stefan Volkwein. “ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation.” In Non-Smooth and Complementarity-Based Distributed Parameter Systems, edited by Hintermüller Michael, Herzog Roland, Kanzow Christian, Ulbrich Michael, and Ulbrich Stefan, 43–76. Cham: Springer, 2022. https://doi.org/10.1007/978-3-030-79393-7_3."},"year":"2022","place":"Cham","author":[{"last_name":"Banholzer","full_name":"Banholzer, Stefan","first_name":"Stefan"},{"first_name":"Bennet","full_name":"Gebken, Bennet","id":"32643","last_name":"Gebken"},{"full_name":"Dellnitz, Michael","last_name":"Dellnitz","first_name":"Michael"},{"orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","id":"47427","full_name":"Peitz, Sebastian","first_name":"Sebastian"},{"full_name":"Volkwein, Stefan","last_name":"Volkwein","first_name":"Stefan"}],"date_created":"2020-03-13T12:45:31Z","date_updated":"2022-03-14T13:04:51Z","publisher":"Springer","oa":"1","doi":"10.1007/978-3-030-79393-7_3","main_file_link":[{"url":"https://arxiv.org/pdf/1906.09075.pdf","open_access":"1"}],"title":"ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation"},{"editor":[{"last_name":"Bock","full_name":"Bock, H. G.","first_name":"H. G."},{"first_name":"K.-H.","last_name":"Küfer","full_name":"Küfer, K.-H."},{"first_name":"P.","full_name":"Maas, P.","last_name":"Maas"},{"first_name":"A.","full_name":"Milde, A.","last_name":"Milde"},{"first_name":"V.","full_name":"Schulz, V.","last_name":"Schulz"}],"status":"public","type":"book_chapter","_id":"30294","department":[{"_id":"101"},{"_id":"655"}],"user_id":"47427","series_title":"Mathematics in Industry","place":"Cham","intvolume":" 35","citation":{"bibtex":"@inbook{Peitz_Dellnitz_Bannenberg_2022, place={Cham}, series={Mathematics in Industry}, title={Efficient Virtual Design and Testing of Autonomous Vehicles}, volume={35}, DOI={10.1007/978-3-030-81455-7_23}, booktitle={German Success Stories in Industrial Mathematics}, publisher={Springer International Publishing}, author={Peitz, Sebastian and Dellnitz, Michael and Bannenberg, Sebastian}, editor={Bock, H. G. and Küfer, K.-H. and Maas, P. and Milde, A. and Schulz, V.}, year={2022}, collection={Mathematics in Industry} }","short":"S. Peitz, M. Dellnitz, S. Bannenberg, in: H.G. Bock, K.-H. Küfer, P. Maas, A. Milde, V. Schulz (Eds.), German Success Stories in Industrial Mathematics, Springer International Publishing, Cham, 2022.","mla":"Peitz, Sebastian, et al. “Efficient Virtual Design and Testing of Autonomous Vehicles.” German Success Stories in Industrial Mathematics, edited by H. G. Bock et al., vol. 35, Springer International Publishing, 2022, doi:10.1007/978-3-030-81455-7_23.","apa":"Peitz, S., Dellnitz, M., & Bannenberg, S. (2022). Efficient Virtual Design and Testing of Autonomous Vehicles. In H. G. Bock, K.-H. Küfer, P. Maas, A. Milde, & V. Schulz (Eds.), German Success Stories in Industrial Mathematics (Vol. 35). Springer International Publishing. https://doi.org/10.1007/978-3-030-81455-7_23","ama":"Peitz S, Dellnitz M, Bannenberg S. Efficient Virtual Design and Testing of Autonomous Vehicles. In: Bock HG, Küfer K-H, Maas P, Milde A, Schulz V, eds. German Success Stories in Industrial Mathematics. Vol 35. Mathematics in Industry. Springer International Publishing; 2022. doi:10.1007/978-3-030-81455-7_23","chicago":"Peitz, Sebastian, Michael Dellnitz, and Sebastian Bannenberg. “Efficient Virtual Design and Testing of Autonomous Vehicles.” In German Success Stories in Industrial Mathematics, edited by H. G. Bock, K.-H. Küfer, P. Maas, A. Milde, and V. Schulz, Vol. 35. Mathematics in Industry. Cham: Springer International Publishing, 2022. https://doi.org/10.1007/978-3-030-81455-7_23.","ieee":"S. Peitz, M. Dellnitz, and S. Bannenberg, “Efficient Virtual Design and Testing of Autonomous Vehicles,” in German Success Stories in Industrial Mathematics, vol. 35, H. G. Bock, K.-H. Küfer, P. Maas, A. Milde, and V. Schulz, Eds. Cham: Springer International Publishing, 2022."},"publication_identifier":{"issn":["1612-3956","2198-3283"],"isbn":["9783030814540","9783030814557"]},"publication_status":"published","doi":"10.1007/978-3-030-81455-7_23","date_updated":"2022-03-14T07:42:01Z","volume":35,"author":[{"full_name":"Peitz, Sebastian","id":"47427","orcid":"0000-0002-3389-793X","last_name":"Peitz","first_name":"Sebastian"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"first_name":"Sebastian","full_name":"Bannenberg, Sebastian","last_name":"Bannenberg"}],"abstract":[{"lang":"eng","text":"With the ever increasing capabilities of sensors and controllers, autonomous driving is quickly becoming a reality. This disruptive change in the automotive industry poses major challenges for manufacturers as well as suppliers as entirely new design and testing strategies have to be developed to remain competitive. Most importantly, the complexity of autonomously driving vehicles in a complex, uncertain, and safety-critical environment requires new testing procedures to cover the almost infinite range of potential scenarios."}],"publication":"German Success Stories in Industrial Mathematics","language":[{"iso":"eng"}],"year":"2022","title":"Efficient Virtual Design and Testing of Autonomous Vehicles","publisher":"Springer International Publishing","date_created":"2022-03-14T07:32:41Z"},{"publication_status":"published","citation":{"apa":"Klus, S., Nüske, F., & Peitz, S. (2022). Koopman analysis of quantum systems. Journal of Physics A: Mathematical and Theoretical, 55(31), 314002. https://doi.org/10.1088/1751-8121/ac7d22","short":"S. Klus, F. Nüske, S. Peitz, Journal of Physics A: Mathematical and Theoretical 55 (2022) 314002.","mla":"Klus, Stefan, et al. “Koopman Analysis of Quantum Systems.” Journal of Physics A: Mathematical and Theoretical, vol. 55, no. 31, IOP Publishing Ltd., 2022, p. 314002, doi:10.1088/1751-8121/ac7d22.","bibtex":"@article{Klus_Nüske_Peitz_2022, title={Koopman analysis of quantum systems}, volume={55}, DOI={10.1088/1751-8121/ac7d22}, number={31}, journal={Journal of Physics A: Mathematical and Theoretical}, publisher={IOP Publishing Ltd.}, author={Klus, Stefan and Nüske, Feliks and Peitz, Sebastian}, year={2022}, pages={314002} }","ama":"Klus S, Nüske F, Peitz S. Koopman analysis of quantum systems. Journal of Physics A: Mathematical and Theoretical. 2022;55(31):314002. doi:10.1088/1751-8121/ac7d22","chicago":"Klus, Stefan, Feliks Nüske, and Sebastian Peitz. “Koopman Analysis of Quantum Systems.” Journal of Physics A: Mathematical and Theoretical 55, no. 31 (2022): 314002. https://doi.org/10.1088/1751-8121/ac7d22.","ieee":"S. Klus, F. Nüske, and S. Peitz, “Koopman analysis of quantum systems,” Journal of Physics A: Mathematical and Theoretical, vol. 55, no. 31, p. 314002, 2022, doi: 10.1088/1751-8121/ac7d22."},"intvolume":" 55","page":"314002","oa":"1","date_updated":"2022-07-18T14:26:41Z","author":[{"first_name":"Stefan","last_name":"Klus","full_name":"Klus, Stefan"},{"first_name":"Feliks","id":"81513","full_name":"Nüske, Feliks","last_name":"Nüske","orcid":"0000-0003-2444-7889"},{"last_name":"Peitz","orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian","id":"47427","first_name":"Sebastian"}],"volume":55,"main_file_link":[{"open_access":"1","url":"https://iopscience.iop.org/article/10.1088/1751-8121/ac7d22/pdf"}],"doi":"10.1088/1751-8121/ac7d22","type":"journal_article","status":"public","_id":"29673","user_id":"47427","department":[{"_id":"655"},{"_id":"101"}],"issue":"31","year":"2022","publisher":"IOP Publishing Ltd.","date_created":"2022-01-31T09:49:40Z","title":"Koopman analysis of quantum systems","publication":"Journal of Physics A: Mathematical and Theoretical","abstract":[{"lang":"eng","text":"Koopman operator theory has been successfully applied to problems from various research areas such as fluid dynamics, molecular dynamics, climate science, engineering, and biology. Applications include detecting metastable or coherent sets, coarse-graining, system identification, and control. There is an intricate connection between dynamical systems driven by stochastic differential equations and quantum mechanics. In this paper, we compare the ground-state transformation and Nelson's stochastic mechanics and demonstrate how data-driven methods developed for the approximation of the Koopman operator can be used to analyze quantum physics problems. Moreover, we exploit the relationship between Schrödinger operators and stochastic control problems to show that modern data-driven methods for stochastic control can be used to solve the stationary or imaginary-time Schrödinger equation. Our findings open up a new avenue towards solving Schrödinger's equation using recently developed tools from data science."}],"external_id":{"arxiv":["2201.12062"]},"language":[{"iso":"eng"}]},{"abstract":[{"lang":"eng","text":"In this article, we build on previous work to present an optimization algorithm for nonlinearly constrained multi-objective optimization problems. The algorithm combines a surrogate-assisted derivative-free trust-region approach with the filter method known from single-objective optimization. Instead of the true objective and constraint functions, so-called fully linear models are employed and we show how to deal with the gradient inexactness in the composite step setting, adapted from single-objective optimization as well. Under standard assumptions, we prove convergence of a subset of iterates to a quasi-stationary point and if constraint qualifications hold, then the limit point is also a KKT-point of the multi-objective problem."}],"status":"public","publication":"arXiv:2208.12094","type":"preprint","language":[{"iso":"eng"}],"_id":"33150","external_id":{"arxiv":["2208.12094"]},"department":[{"_id":"101"},{"_id":"655"}],"user_id":"47427","year":"2022","citation":{"apa":"Berkemeier, M. B., & Peitz, S. (2022). Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients. In arXiv:2208.12094.","short":"M.B. Berkemeier, S. Peitz, ArXiv:2208.12094 (2022).","mla":"Berkemeier, Manuel Bastian, and Sebastian Peitz. “Multi-Objective Trust-Region Filter Method for Nonlinear Constraints Using Inexact Gradients.” ArXiv:2208.12094, 2022.","bibtex":"@article{Berkemeier_Peitz_2022, title={Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients}, journal={arXiv:2208.12094}, author={Berkemeier, Manuel Bastian and Peitz, Sebastian}, year={2022} }","ieee":"M. B. Berkemeier and S. Peitz, “Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients,” arXiv:2208.12094. 2022.","chicago":"Berkemeier, Manuel Bastian, and Sebastian Peitz. “Multi-Objective Trust-Region Filter Method for Nonlinear Constraints Using Inexact Gradients.” ArXiv:2208.12094, 2022.","ama":"Berkemeier MB, Peitz S. Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients. arXiv:220812094. Published online 2022."},"title":"Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients","main_file_link":[{"url":"https://arxiv.org/pdf/2208.12094","open_access":"1"}],"date_updated":"2022-08-26T06:12:10Z","oa":"1","date_created":"2022-08-26T06:08:06Z","author":[{"id":"51701","full_name":"Berkemeier, Manuel Bastian","last_name":"Berkemeier","first_name":"Manuel Bastian"},{"first_name":"Sebastian","last_name":"Peitz","orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian","id":"47427"}]},{"abstract":[{"lang":"eng","text":"We present a novel algorithm that allows us to gain detailed insight into the effects of sparsity in linear and nonlinear optimization, which is of great importance in many scientific areas such as image and signal processing, medical imaging, compressed sensing, and machine learning (e.g., for the training of neural networks). Sparsity is an important feature to ensure robustness against noisy data, but also to find models that are interpretable and easy to analyze due to the small number of relevant terms. It is common practice to enforce sparsity by adding the ℓ1-norm as a weighted penalty term. In order to gain a better understanding and to allow for an informed model selection, we directly solve the corresponding multiobjective optimization problem (MOP) that arises when we minimize the main objective and the ℓ1-norm simultaneously. As this MOP is in general non-convex for nonlinear objectives, the weighting method will fail to provide all optimal compromises. To avoid this issue, we present a continuation method which is specifically tailored to MOPs with two objective functions one of which is the ℓ1-norm. Our method can be seen as a generalization of well-known homotopy methods for linear regression problems to the nonlinear case. Several numerical examples - including neural network training - demonstrate our theoretical findings and the additional insight that can be gained by this multiobjective approach."}],"file":[{"content_type":"application/pdf","relation":"main_file","success":1,"creator":"speitz","date_created":"2021-09-25T11:59:15Z","date_updated":"2021-09-25T11:59:15Z","access_level":"closed","file_name":"On_the_Treatment_of_Optimization_Problems_with_L1_Penalty_Terms_via_Multiobjective_Continuation.pdf","file_id":"25040","file_size":7990831}],"publication":"IEEE Transactions on Pattern Analysis and Machine Intelligence","ddc":["510"],"language":[{"iso":"eng"}],"year":"2022","issue":"11","title":"On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation","publisher":"IEEE","date_created":"2020-12-15T07:46:36Z","status":"public","type":"journal_article","article_type":"original","file_date_updated":"2021-09-25T11:59:15Z","_id":"20731","user_id":"47427","department":[{"_id":"101"},{"_id":"530"},{"_id":"655"}],"citation":{"chicago":"Bieker, Katharina, Bennet Gebken, and Sebastian Peitz. “On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation.” IEEE Transactions on Pattern Analysis and Machine Intelligence 44, no. 11 (2022): 7797–7808. https://doi.org/10.1109/TPAMI.2021.3114962.","ieee":"K. Bieker, B. Gebken, and S. Peitz, “On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 44, no. 11, pp. 7797–7808, 2022, doi: 10.1109/TPAMI.2021.3114962.","ama":"Bieker K, Gebken B, Peitz S. On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2022;44(11):7797-7808. doi:10.1109/TPAMI.2021.3114962","apa":"Bieker, K., Gebken, B., & Peitz, S. (2022). On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 44(11), 7797–7808. https://doi.org/10.1109/TPAMI.2021.3114962","short":"K. Bieker, B. Gebken, S. Peitz, IEEE Transactions on Pattern Analysis and Machine Intelligence 44 (2022) 7797–7808.","bibtex":"@article{Bieker_Gebken_Peitz_2022, title={On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation}, volume={44}, DOI={10.1109/TPAMI.2021.3114962}, number={11}, journal={IEEE Transactions on Pattern Analysis and Machine Intelligence}, publisher={IEEE}, author={Bieker, Katharina and Gebken, Bennet and Peitz, Sebastian}, year={2022}, pages={7797–7808} }","mla":"Bieker, Katharina, et al. “On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation.” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 44, no. 11, IEEE, 2022, pp. 7797–808, doi:10.1109/TPAMI.2021.3114962."},"intvolume":" 44","page":"7797-7808","publication_status":"epub_ahead","has_accepted_license":"1","main_file_link":[{"open_access":"1","url":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9547772"}],"doi":"10.1109/TPAMI.2021.3114962","oa":"1","date_updated":"2022-10-21T12:27:16Z","author":[{"full_name":"Bieker, Katharina","id":"32829","last_name":"Bieker","first_name":"Katharina"},{"last_name":"Gebken","id":"32643","full_name":"Gebken, Bennet","first_name":"Bennet"},{"last_name":"Peitz","orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian","id":"47427","first_name":"Sebastian"}],"volume":44},{"citation":{"ama":"Wohlleben MC, Bender A, Peitz S, Sextro W. Development of a Hybrid Modeling Methodology for Oscillating Systems with Friction. In: Machine Learning, Optimization, and Data Science. Springer International Publishing; 2022. doi:10.1007/978-3-030-95470-3_8","ieee":"M. C. Wohlleben, A. Bender, S. Peitz, and W. Sextro, “Development of a Hybrid Modeling Methodology for Oscillating Systems with Friction,” in Machine Learning, Optimization, and Data Science, Cham: Springer International Publishing, 2022.","chicago":"Wohlleben, Meike Claudia, Amelie Bender, Sebastian Peitz, and Walter Sextro. “Development of a Hybrid Modeling Methodology for Oscillating Systems with Friction.” In Machine Learning, Optimization, and Data Science. Cham: Springer International Publishing, 2022. https://doi.org/10.1007/978-3-030-95470-3_8.","bibtex":"@inbook{Wohlleben_Bender_Peitz_Sextro_2022, place={Cham}, title={Development of a Hybrid Modeling Methodology for Oscillating Systems with Friction}, DOI={10.1007/978-3-030-95470-3_8}, booktitle={Machine Learning, Optimization, and Data Science}, publisher={Springer International Publishing}, author={Wohlleben, Meike Claudia and Bender, Amelie and Peitz, Sebastian and Sextro, Walter}, year={2022} }","short":"M.C. Wohlleben, A. Bender, S. Peitz, W. Sextro, in: Machine Learning, Optimization, and Data Science, Springer International Publishing, Cham, 2022.","mla":"Wohlleben, Meike Claudia, et al. “Development of a Hybrid Modeling Methodology for Oscillating Systems with Friction.” Machine Learning, Optimization, and Data Science, Springer International Publishing, 2022, doi:10.1007/978-3-030-95470-3_8.","apa":"Wohlleben, M. C., Bender, A., Peitz, S., & Sextro, W. (2022). Development of a Hybrid Modeling Methodology for Oscillating Systems with Friction. In Machine Learning, Optimization, and Data Science. Springer International Publishing. https://doi.org/10.1007/978-3-030-95470-3_8"},"year":"2022","place":"Cham","quality_controlled":"1","publication_identifier":{"issn":["0302-9743","1611-3349"],"isbn":["9783030954697","9783030954703"]},"publication_status":"published","doi":"10.1007/978-3-030-95470-3_8","main_file_link":[{"url":"https://link.springer.com/content/pdf/10.1007%2F978-3-030-95470-3_8.pdf"}],"title":"Development of a Hybrid Modeling Methodology for Oscillating Systems with Friction","author":[{"full_name":"Wohlleben, Meike Claudia","id":"43991","last_name":"Wohlleben","first_name":"Meike Claudia"},{"id":"54290","full_name":"Bender, Amelie","last_name":"Bender","first_name":"Amelie"},{"full_name":"Peitz, Sebastian","id":"47427","last_name":"Peitz","orcid":"0000-0002-3389-793X","first_name":"Sebastian"},{"last_name":"Sextro","id":"21220","full_name":"Sextro, Walter","first_name":"Walter"}],"date_created":"2022-02-03T10:30:23Z","publisher":"Springer International Publishing","date_updated":"2023-04-26T12:10:58Z","status":"public","publication":"Machine Learning, Optimization, and Data Science","type":"book_chapter","language":[{"iso":"eng"}],"department":[{"_id":"151"},{"_id":"655"}],"user_id":"43991","_id":"29727"},{"date_created":"2021-03-01T10:46:48Z","title":"Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models","issue":"2","year":"2021","language":[{"iso":"eng"}],"publication":"Mathematical and Computational Applications","abstract":[{"text":"We present a flexible trust region descend algorithm for unconstrained and\r\nconvexly constrained multiobjective optimization problems. It is targeted at\r\nheterogeneous and expensive problems, i.e., problems that have at least one\r\nobjective function that is computationally expensive. The method is\r\nderivative-free in the sense that neither need derivative information be\r\navailable for the expensive objectives nor are gradients approximated using\r\nrepeated function evaluations as is the case in finite-difference methods.\r\nInstead, a multiobjective trust region approach is used that works similarly to\r\nits well-known scalar pendants. Local surrogate models constructed from\r\nevaluation data of the true objective functions are employed to compute\r\npossible descent directions. In contrast to existing multiobjective trust\r\nregion algorithms, these surrogates are not polynomial but carefully\r\nconstructed radial basis function networks. This has the important advantage\r\nthat the number of data points scales linearly with the parameter space\r\ndimension. The local models qualify as fully linear and the corresponding\r\ngeneral scalar framework is adapted for problems with multiple objectives.\r\nConvergence to Pareto critical points is proven and numerical examples\r\nillustrate our findings.","lang":"eng"}],"volume":26,"author":[{"last_name":"Berkemeier","full_name":"Berkemeier, Manuel Bastian","id":"51701","first_name":"Manuel Bastian"},{"first_name":"Sebastian","last_name":"Peitz","orcid":"0000-0002-3389-793X","id":"47427","full_name":"Peitz, Sebastian"}],"date_updated":"2022-01-06T06:54:55Z","oa":"1","doi":"10.3390/mca26020031","main_file_link":[{"open_access":"1","url":"https://www.mdpi.com/2297-8747/26/2/31/pdf"}],"publication_identifier":{"eissn":["2297-8747"]},"publication_status":"published","intvolume":" 26","citation":{"ama":"Berkemeier MB, Peitz S. Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models. Mathematical and Computational Applications. 2021;26(2). doi:10.3390/mca26020031","chicago":"Berkemeier, Manuel Bastian, and Sebastian Peitz. “Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models.” Mathematical and Computational Applications 26, no. 2 (2021). https://doi.org/10.3390/mca26020031.","ieee":"M. B. Berkemeier and S. Peitz, “Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models,” Mathematical and Computational Applications, vol. 26, no. 2, 2021.","bibtex":"@article{Berkemeier_Peitz_2021, title={Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models}, volume={26}, DOI={10.3390/mca26020031}, number={231}, journal={Mathematical and Computational Applications}, author={Berkemeier, Manuel Bastian and Peitz, Sebastian}, year={2021} }","mla":"Berkemeier, Manuel Bastian, and Sebastian Peitz. “Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models.” Mathematical and Computational Applications, vol. 26, no. 2, 31, 2021, doi:10.3390/mca26020031.","short":"M.B. Berkemeier, S. Peitz, Mathematical and Computational Applications 26 (2021).","apa":"Berkemeier, M. B., & Peitz, S. (2021). Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models. Mathematical and Computational Applications, 26(2). https://doi.org/10.3390/mca26020031"},"department":[{"_id":"101"},{"_id":"655"}],"user_id":"47427","_id":"21337","article_number":"31","type":"journal_article","status":"public"},{"type":"journal_article","publication":"Journal of Optimization Theory and Applications","abstract":[{"lang":"eng","text":"In this article, we present an efficient descent method for locally Lipschitz\r\ncontinuous multiobjective optimization problems (MOPs). The method is realized\r\nby combining a theoretical result regarding the computation of descent\r\ndirections for nonsmooth MOPs with a practical method to approximate the\r\nsubdifferentials of the objective functions. We show convergence to points\r\nwhich satisfy a necessary condition for Pareto optimality. Using a set of test\r\nproblems, we compare our method to the multiobjective proximal bundle method by\r\nM\\\"akel\\\"a. The results indicate that our method is competitive while being\r\neasier to implement. While the number of objective function evaluations is\r\nlarger, the overall number of subgradient evaluations is lower. Finally, we\r\nshow that our method can be combined with a subdivision algorithm to compute\r\nentire Pareto sets of nonsmooth MOPs."}],"status":"public","_id":"16867","user_id":"47427","department":[{"_id":"101"}],"language":[{"iso":"eng"}],"publication_status":"published","year":"2021","citation":{"ama":"Gebken B, Peitz S. An efficient descent method for locally Lipschitz multiobjective optimization problems. Journal of Optimization Theory and Applications. 2021;188:696-723. doi:10.1007/s10957-020-01803-w","chicago":"Gebken, Bennet, and Sebastian Peitz. “An Efficient Descent Method for Locally Lipschitz Multiobjective Optimization Problems.” Journal of Optimization Theory and Applications 188 (2021): 696–723. https://doi.org/10.1007/s10957-020-01803-w.","ieee":"B. Gebken and S. Peitz, “An efficient descent method for locally Lipschitz multiobjective optimization problems,” Journal of Optimization Theory and Applications, vol. 188, pp. 696–723, 2021.","bibtex":"@article{Gebken_Peitz_2021, title={An efficient descent method for locally Lipschitz multiobjective optimization problems}, volume={188}, DOI={10.1007/s10957-020-01803-w}, journal={Journal of Optimization Theory and Applications}, author={Gebken, Bennet and Peitz, Sebastian}, year={2021}, pages={696–723} }","mla":"Gebken, Bennet, and Sebastian Peitz. “An Efficient Descent Method for Locally Lipschitz Multiobjective Optimization Problems.” Journal of Optimization Theory and Applications, vol. 188, 2021, pp. 696–723, doi:10.1007/s10957-020-01803-w.","short":"B. Gebken, S. Peitz, Journal of Optimization Theory and Applications 188 (2021) 696–723.","apa":"Gebken, B., & Peitz, S. (2021). An efficient descent method for locally Lipschitz multiobjective optimization problems. Journal of Optimization Theory and Applications, 188, 696–723. https://doi.org/10.1007/s10957-020-01803-w"},"intvolume":" 188","page":"696-723","oa":"1","date_updated":"2022-01-06T06:52:57Z","author":[{"last_name":"Gebken","id":"32643","full_name":"Gebken, Bennet","first_name":"Bennet"},{"first_name":"Sebastian","last_name":"Peitz","orcid":"0000-0002-3389-793X","id":"47427","full_name":"Peitz, Sebastian"}],"date_created":"2020-04-27T09:11:22Z","volume":188,"title":"An efficient descent method for locally Lipschitz multiobjective optimization problems","main_file_link":[{"open_access":"1","url":"https://link.springer.com/content/pdf/10.1007/s10957-020-01803-w.pdf"}],"doi":"10.1007/s10957-020-01803-w"},{"language":[{"iso":"eng"}],"_id":"16295","user_id":"47427","department":[{"_id":"101"}],"abstract":[{"lang":"eng","text":"It is a challenging task to identify the objectives on which a certain decision was based, in particular if several, potentially conflicting criteria are equally important and a continuous set of optimal compromise decisions exists. This task can be understood as the inverse problem of multiobjective optimization, where the goal is to find the objective function vector of a given Pareto set. To this end, we present a method to construct the objective function vector of an unconstrained multiobjective optimization problem (MOP) such that the Pareto critical set contains a given set of data points with prescribed KKT multipliers. If such an MOP can not be found, then the method instead produces an MOP whose Pareto critical set is at least close to the data points. The key idea is to consider the objective function vector in the multiobjective KKT conditions as variable and then search for the objectives that minimize the Euclidean norm of the resulting system of equations. By expressing the objectives in a finite-dimensional basis, we transform this problem into a homogeneous, linear system of equations that can be solved efficiently. Potential applications of this approach include the identification of objectives (both from clean and noisy data) and the construction of surrogate models for expensive MOPs."}],"status":"public","type":"journal_article","publication":"Journal of Global Optimization","title":"Inverse multiobjective optimization: Inferring decision criteria from data","main_file_link":[{"open_access":"1","url":"https://link.springer.com/content/pdf/10.1007/s10898-020-00983-z.pdf"}],"doi":"10.1007/s10898-020-00983-z","oa":"1","date_updated":"2022-01-06T06:52:48Z","publisher":"Springer","author":[{"first_name":"Bennet","last_name":"Gebken","full_name":"Gebken, Bennet","id":"32643"},{"first_name":"Sebastian","last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian","id":"47427"}],"date_created":"2020-03-13T12:45:05Z","volume":80,"year":"2021","citation":{"ama":"Gebken B, Peitz S. Inverse multiobjective optimization: Inferring decision criteria from data. Journal of Global Optimization. 2021;80:3-29. doi:10.1007/s10898-020-00983-z","chicago":"Gebken, Bennet, and Sebastian Peitz. “Inverse Multiobjective Optimization: Inferring Decision Criteria from Data.” Journal of Global Optimization 80 (2021): 3–29. https://doi.org/10.1007/s10898-020-00983-z.","ieee":"B. Gebken and S. Peitz, “Inverse multiobjective optimization: Inferring decision criteria from data,” Journal of Global Optimization, vol. 80, pp. 3–29, 2021.","short":"B. Gebken, S. Peitz, Journal of Global Optimization 80 (2021) 3–29.","mla":"Gebken, Bennet, and Sebastian Peitz. “Inverse Multiobjective Optimization: Inferring Decision Criteria from Data.” Journal of Global Optimization, vol. 80, Springer, 2021, pp. 3–29, doi:10.1007/s10898-020-00983-z.","bibtex":"@article{Gebken_Peitz_2021, title={Inverse multiobjective optimization: Inferring decision criteria from data}, volume={80}, DOI={10.1007/s10898-020-00983-z}, journal={Journal of Global Optimization}, publisher={Springer}, author={Gebken, Bennet and Peitz, Sebastian}, year={2021}, pages={3–29} }","apa":"Gebken, B., & Peitz, S. (2021). Inverse multiobjective optimization: Inferring decision criteria from data. Journal of Global Optimization, 80, 3–29. https://doi.org/10.1007/s10898-020-00983-z"},"page":"3-29","intvolume":" 80"},{"date_updated":"2022-01-24T13:27:50Z","oa":"1","date_created":"2020-03-13T12:44:36Z","author":[{"first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina"},{"full_name":"Peitz, Sebastian","id":"47427","last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X","first_name":"Sebastian"}],"volume":"31(2)","title":"Explicit multiobjective model predictive control for nonlinear systems with symmetries","main_file_link":[{"open_access":"1","url":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/rnc.5281"}],"doi":"10.1002/rnc.5281","year":"2021","citation":{"bibtex":"@article{Ober-Blöbaum_Peitz_2021, title={Explicit multiobjective model predictive control for nonlinear systems with symmetries}, volume={31(2)}, DOI={10.1002/rnc.5281}, journal={International Journal of Robust and Nonlinear Control}, author={Ober-Blöbaum, Sina and Peitz, Sebastian}, year={2021}, pages={380–403} }","short":"S. Ober-Blöbaum, S. Peitz, International Journal of Robust and Nonlinear Control 31(2) (2021) 380–403.","mla":"Ober-Blöbaum, Sina, and Sebastian Peitz. “Explicit Multiobjective Model Predictive Control for Nonlinear Systems with Symmetries.” International Journal of Robust and Nonlinear Control, vol. 31(2), 2021, pp. 380–403, doi:10.1002/rnc.5281.","apa":"Ober-Blöbaum, S., & Peitz, S. (2021). Explicit multiobjective model predictive control for nonlinear systems with symmetries. International Journal of Robust and Nonlinear Control, 31(2), 380–403. https://doi.org/10.1002/rnc.5281","ama":"Ober-Blöbaum S, Peitz S. Explicit multiobjective model predictive control for nonlinear systems with symmetries. International Journal of Robust and Nonlinear Control. 2021;31(2):380-403. doi:10.1002/rnc.5281","ieee":"S. Ober-Blöbaum and S. Peitz, “Explicit multiobjective model predictive control for nonlinear systems with symmetries,” International Journal of Robust and Nonlinear Control, vol. 31(2), pp. 380–403, 2021, doi: 10.1002/rnc.5281.","chicago":"Ober-Blöbaum, Sina, and Sebastian Peitz. “Explicit Multiobjective Model Predictive Control for Nonlinear Systems with Symmetries.” International Journal of Robust and Nonlinear Control 31(2) (2021): 380–403. https://doi.org/10.1002/rnc.5281."},"page":"380-403","project":[{"_id":"52","name":"Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"_id":"16294","user_id":"15694","department":[{"_id":"101"}],"language":[{"iso":"eng"}],"type":"journal_article","publication":"International Journal of Robust and Nonlinear Control","abstract":[{"text":"Model predictive control is a prominent approach to construct a feedback\r\ncontrol loop for dynamical systems. Due to real-time constraints, the major\r\nchallenge in MPC is to solve model-based optimal control problems in a very\r\nshort amount of time. For linear-quadratic problems, Bemporad et al. have\r\nproposed an explicit formulation where the underlying optimization problems are\r\nsolved a priori in an offline phase. In this article, we present an extension\r\nof this concept in two significant ways. We consider nonlinear problems and -\r\nmore importantly - problems with multiple conflicting objective functions. In\r\nthe offline phase, we build a library of Pareto optimal solutions from which we\r\nthen obtain a valid compromise solution in the online phase according to a\r\ndecision maker's preference. Since the standard multi-parametric programming\r\napproach is no longer valid in this situation, we instead use interpolation\r\nbetween different entries of the library. To reduce the number of problems that\r\nhave to be solved in the offline phase, we exploit symmetries in the dynamical\r\nsystem and the corresponding multiobjective optimal control problem. The\r\nresults are verified using two different examples from autonomous driving.","lang":"eng"}],"status":"public"},{"_id":"17411","department":[{"_id":"101"}],"user_id":"47427","language":[{"iso":"eng"}],"publication":"Advances in Dynamics, Optimization and Computation","type":"book_chapter","editor":[{"full_name":"Junge, Oliver","last_name":"Junge","first_name":"Oliver"},{"full_name":"Schütze, Oliver","last_name":"Schütze","first_name":"Oliver"},{"last_name":"Froyland","full_name":"Froyland, Gary","first_name":"Gary"},{"first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina"},{"full_name":"Padberg-Gehle, Kathrin","last_name":"Padberg-Gehle","first_name":"Kathrin"}],"abstract":[{"text":"Many dynamical systems possess symmetries, e.g. rotational and translational invariances of mechanical systems. These can be beneficially exploited in the design of numerical optimal control methods. We present a model predictive control scheme which is based on a library of precomputed motion primitives. The primitives are equivalence classes w.r.t. the symmetry of the optimal control problems. Trim primitives as relative equilibria w.r.t. this symmetry, play a crucial role in the algorithm. The approach is illustrated using an academic mobile robot example.","lang":"eng"}],"status":"public","date_updated":"2022-01-06T06:53:11Z","publisher":"Springer","author":[{"first_name":"Kathrin","last_name":"Flaßkamp","full_name":"Flaßkamp, Kathrin"},{"first_name":"Sina","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum"},{"last_name":"Peitz","orcid":"0000-0002-3389-793X","id":"47427","full_name":"Peitz, Sebastian","first_name":"Sebastian"}],"date_created":"2020-07-27T09:50:19Z","title":"Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach","doi":"10.1007/978-3-030-51264-4_9","publication_identifier":{"issn":["2198-4182","2198-4190"],"isbn":["9783030512637","9783030512644"]},"publication_status":"published","year":"2020","place":"Cham","citation":{"apa":"Flaßkamp, K., Ober-Blöbaum, S., & Peitz, S. (2020). Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach. In O. Junge, O. Schütze, G. Froyland, S. Ober-Blöbaum, & K. Padberg-Gehle (Eds.), Advances in Dynamics, Optimization and Computation. Cham: Springer. https://doi.org/10.1007/978-3-030-51264-4_9","bibtex":"@inbook{Flaßkamp_Ober-Blöbaum_Peitz_2020, place={Cham}, title={Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach}, DOI={10.1007/978-3-030-51264-4_9}, booktitle={Advances in Dynamics, Optimization and Computation}, publisher={Springer}, author={Flaßkamp, Kathrin and Ober-Blöbaum, Sina and Peitz, Sebastian}, editor={Junge, Oliver and Schütze, Oliver and Froyland, Gary and Ober-Blöbaum, Sina and Padberg-Gehle, KathrinEditors}, year={2020} }","mla":"Flaßkamp, Kathrin, et al. “Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach.” Advances in Dynamics, Optimization and Computation, edited by Oliver Junge et al., Springer, 2020, doi:10.1007/978-3-030-51264-4_9.","short":"K. Flaßkamp, S. Ober-Blöbaum, S. Peitz, in: O. Junge, O. Schütze, G. Froyland, S. Ober-Blöbaum, K. Padberg-Gehle (Eds.), Advances in Dynamics, Optimization and Computation, Springer, Cham, 2020.","ama":"Flaßkamp K, Ober-Blöbaum S, Peitz S. Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach. In: Junge O, Schütze O, Froyland G, Ober-Blöbaum S, Padberg-Gehle K, eds. Advances in Dynamics, Optimization and Computation. Cham: Springer; 2020. doi:10.1007/978-3-030-51264-4_9","chicago":"Flaßkamp, Kathrin, Sina Ober-Blöbaum, and Sebastian Peitz. “Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach.” In Advances in Dynamics, Optimization and Computation, edited by Oliver Junge, Oliver Schütze, Gary Froyland, Sina Ober-Blöbaum, and Kathrin Padberg-Gehle. Cham: Springer, 2020. https://doi.org/10.1007/978-3-030-51264-4_9.","ieee":"K. Flaßkamp, S. Ober-Blöbaum, and S. Peitz, “Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach,” in Advances in Dynamics, Optimization and Computation, O. Junge, O. Schütze, G. Froyland, S. Ober-Blöbaum, and K. Padberg-Gehle, Eds. Cham: Springer, 2020."}},{"doi":"10.1080/0305215x.2019.1617286","title":"Pareto Explorer: a global/local exploration tool for many-objective optimization problems","date_created":"2019-07-10T08:14:39Z","author":[{"first_name":"Oliver","full_name":"Schütze, Oliver","last_name":"Schütze"},{"first_name":"Oliver","last_name":"Cuate","full_name":"Cuate, Oliver"},{"full_name":"Martín, Adanay","last_name":"Martín","first_name":"Adanay"},{"id":"47427","full_name":"Peitz, Sebastian","last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X","first_name":"Sebastian"},{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"}],"volume":52,"date_updated":"2022-01-06T06:50:46Z","citation":{"ama":"Schütze O, Cuate O, Martín A, Peitz S, Dellnitz M. Pareto Explorer: a global/local exploration tool for many-objective optimization problems. Engineering Optimization. 2020;52(5):832-855. doi:10.1080/0305215x.2019.1617286","ieee":"O. Schütze, O. Cuate, A. Martín, S. Peitz, and M. Dellnitz, “Pareto Explorer: a global/local exploration tool for many-objective optimization problems,” Engineering Optimization, vol. 52, no. 5, pp. 832–855, 2020.","chicago":"Schütze, Oliver, Oliver Cuate, Adanay Martín, Sebastian Peitz, and Michael Dellnitz. “Pareto Explorer: A Global/Local Exploration Tool for Many-Objective Optimization Problems.” Engineering Optimization 52, no. 5 (2020): 832–55. https://doi.org/10.1080/0305215x.2019.1617286.","mla":"Schütze, Oliver, et al. “Pareto Explorer: A Global/Local Exploration Tool for Many-Objective Optimization Problems.” Engineering Optimization, vol. 52, no. 5, 2020, pp. 832–55, doi:10.1080/0305215x.2019.1617286.","short":"O. Schütze, O. Cuate, A. Martín, S. Peitz, M. Dellnitz, Engineering Optimization 52 (2020) 832–855.","bibtex":"@article{Schütze_Cuate_Martín_Peitz_Dellnitz_2020, title={Pareto Explorer: a global/local exploration tool for many-objective optimization problems}, volume={52}, DOI={10.1080/0305215x.2019.1617286}, number={5}, journal={Engineering Optimization}, author={Schütze, Oliver and Cuate, Oliver and Martín, Adanay and Peitz, Sebastian and Dellnitz, Michael}, year={2020}, pages={832–855} }","apa":"Schütze, O., Cuate, O., Martín, A., Peitz, S., & Dellnitz, M. (2020). Pareto Explorer: a global/local exploration tool for many-objective optimization problems. Engineering Optimization, 52(5), 832–855. https://doi.org/10.1080/0305215x.2019.1617286"},"intvolume":" 52","page":"832-855","year":"2020","issue":"5","publication_status":"published","publication_identifier":{"issn":["0305-215X","1029-0273"]},"language":[{"iso":"eng"}],"article_type":"original","user_id":"47427","department":[{"_id":"101"}],"_id":"10596","status":"public","abstract":[{"lang":"eng","text":"Multi-objective optimization is an active field of research that has many applications. Owing to its success and because decision-making processes are becoming more and more complex, there is a recent trend for incorporating many objectives into such problems. The challenge with such problems, however, is that the dimensions of the solution sets—the so-called Pareto sets and fronts—grow with the number of objectives. It is thus no longer possible to compute or to approximate the entire solution set of a given problem that contains many (e.g. more than three) objectives. On the other hand, the computation of single solutions (e.g. via scalarization methods) leads to unsatisfying results in many cases, even if user preferences are incorporated. In this article, the Pareto Explorer tool is presented—a global/local exploration tool for the treatment of many-objective optimization problems (MaOPs). In the first step, a solution of the problem is computed via a global search algorithm that ideally already includes user preferences. In the second step, a local search along the Pareto set/front of the given MaOP is performed in user specified directions. For this, several continuation-like procedures are proposed that can incorporate preferences defined in decision, objective, or in weight space. The applicability and usefulness of Pareto Explorer is demonstrated on benchmark problems as well as on an application from industrial laundry design."}],"type":"journal_article","publication":"Engineering Optimization"},{"title":"Data-driven approximation of the Koopman generator: Model reduction, system identification, and control","doi":"10.1016/j.physd.2020.132416","date_updated":"2022-01-06T06:52:48Z","volume":406,"author":[{"first_name":"Stefan","last_name":"Klus","full_name":"Klus, Stefan"},{"first_name":"Feliks","orcid":"0000-0003-2444-7889","last_name":"Nüske","id":"81513","full_name":"Nüske, Feliks"},{"orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","full_name":"Peitz, Sebastian","id":"47427","first_name":"Sebastian"},{"first_name":"Jan-Hendrik","last_name":"Niemann","full_name":"Niemann, Jan-Hendrik"},{"first_name":"Cecilia","full_name":"Clementi, Cecilia","last_name":"Clementi"},{"first_name":"Christof","last_name":"Schütte","full_name":"Schütte, Christof"}],"date_created":"2020-03-13T12:35:40Z","year":"2020","intvolume":" 406","citation":{"mla":"Klus, Stefan, et al. “Data-Driven Approximation of the Koopman Generator: Model Reduction, System Identification, and Control.” Physica D: Nonlinear Phenomena, vol. 406, 132416, 2020, doi:10.1016/j.physd.2020.132416.","short":"S. Klus, F. Nüske, S. Peitz, J.-H. Niemann, C. Clementi, C. Schütte, Physica D: Nonlinear Phenomena 406 (2020).","bibtex":"@article{Klus_Nüske_Peitz_Niemann_Clementi_Schütte_2020, title={Data-driven approximation of the Koopman generator: Model reduction, system identification, and control}, volume={406}, DOI={10.1016/j.physd.2020.132416}, number={132416}, journal={Physica D: Nonlinear Phenomena}, author={Klus, Stefan and Nüske, Feliks and Peitz, Sebastian and Niemann, Jan-Hendrik and Clementi, Cecilia and Schütte, Christof}, year={2020} }","apa":"Klus, S., Nüske, F., Peitz, S., Niemann, J.-H., Clementi, C., & Schütte, C. (2020). Data-driven approximation of the Koopman generator: Model reduction, system identification, and control. Physica D: Nonlinear Phenomena, 406. https://doi.org/10.1016/j.physd.2020.132416","ama":"Klus S, Nüske F, Peitz S, Niemann J-H, Clementi C, Schütte C. Data-driven approximation of the Koopman generator: Model reduction, system identification, and control. Physica D: Nonlinear Phenomena. 2020;406. doi:10.1016/j.physd.2020.132416","ieee":"S. Klus, F. Nüske, S. Peitz, J.-H. Niemann, C. Clementi, and C. Schütte, “Data-driven approximation of the Koopman generator: Model reduction, system identification, and control,” Physica D: Nonlinear Phenomena, vol. 406, 2020.","chicago":"Klus, Stefan, Feliks Nüske, Sebastian Peitz, Jan-Hendrik Niemann, Cecilia Clementi, and Christof Schütte. “Data-Driven Approximation of the Koopman Generator: Model Reduction, System Identification, and Control.” Physica D: Nonlinear Phenomena 406 (2020). https://doi.org/10.1016/j.physd.2020.132416."},"publication_identifier":{"issn":["0167-2789"]},"publication_status":"published","article_number":"132416","language":[{"iso":"eng"}],"_id":"16288","department":[{"_id":"101"}],"user_id":"47427","abstract":[{"lang":"eng","text":"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."}],"status":"public","publication":"Physica D: Nonlinear Phenomena","type":"journal_article"}]