--- _id: '21199' abstract: - lang: eng text: "As in almost every other branch of science, the major advances in data\r\nscience and machine learning have also resulted in significant improvements\r\nregarding the modeling and simulation of nonlinear dynamical systems. It is\r\nnowadays possible to make accurate medium to long-term predictions of highly\r\ncomplex systems such as the weather, the dynamics within a nuclear fusion\r\nreactor, of disease models or the stock market in a very efficient manner. In\r\nmany cases, predictive methods are advertised to ultimately be useful for\r\ncontrol, as the control of high-dimensional nonlinear systems is an engineering\r\ngrand challenge with huge potential in areas such as clean and efficient energy\r\nproduction, or the development of advanced medical devices. However, the\r\nquestion of how to use a predictive model for control is often left unanswered\r\ndue to the associated challenges, namely a significantly higher system\r\ncomplexity, the requirement of much larger data sets and an increased and often\r\nproblem-specific modeling effort. To solve these issues, we present a universal\r\nframework (which we call QuaSiModO:\r\nQuantization-Simulation-Modeling-Optimization) to transform arbitrary\r\npredictive models into control systems and use them for feedback control. The\r\nadvantages of our approach are a linear increase in data requirements with\r\nrespect to the control dimension, performance guarantees that rely exclusively\r\non the accuracy of the predictive model, and only little prior knowledge\r\nrequirements in control theory to solve complex control problems. In particular\r\nthe latter point is of key importance to enable a large number of researchers\r\nand practitioners to exploit the ever increasing capabilities of predictive\r\nmodels for control in a straight-forward and systematic fashion." article_number: '110840' author: - first_name: Sebastian full_name: Peitz, Sebastian id: '47427' last_name: Peitz orcid: 0000-0002-3389-793X - first_name: Katharina full_name: Bieker, Katharina id: '32829' last_name: Bieker citation: ama: Peitz S, Bieker K. On the Universal Transformation of Data-Driven Models to Control Systems. Automatica. 2023;149. doi:10.1016/j.automatica.2022.110840 apa: Peitz, S., & Bieker, K. (2023). On the Universal Transformation of Data-Driven Models to Control Systems. Automatica, 149, Article 110840. https://doi.org/10.1016/j.automatica.2022.110840 bibtex: '@article{Peitz_Bieker_2023, title={On the Universal Transformation of Data-Driven Models to Control Systems}, volume={149}, DOI={10.1016/j.automatica.2022.110840}, number={110840}, journal={Automatica}, publisher={Elsevier}, author={Peitz, Sebastian and Bieker, Katharina}, year={2023} }' chicago: Peitz, Sebastian, and Katharina Bieker. “On the Universal Transformation of Data-Driven Models to Control Systems.” Automatica 149 (2023). https://doi.org/10.1016/j.automatica.2022.110840. ieee: 'S. Peitz and K. Bieker, “On the Universal Transformation of Data-Driven Models to Control Systems,” Automatica, vol. 149, Art. no. 110840, 2023, doi: 10.1016/j.automatica.2022.110840.' mla: Peitz, Sebastian, and Katharina Bieker. “On the Universal Transformation of Data-Driven Models to Control Systems.” Automatica, vol. 149, 110840, Elsevier, 2023, doi:10.1016/j.automatica.2022.110840. short: S. Peitz, K. Bieker, Automatica 149 (2023). date_created: 2021-02-10T07:04:15Z date_updated: 2023-01-07T12:01:58Z department: - _id: '101' - _id: '655' doi: 10.1016/j.automatica.2022.110840 intvolume: ' 149' language: - iso: eng main_file_link: - open_access: '1' url: https://www.sciencedirect.com/science/article/pii/S0005109822007075/pdfft?isDTMRedir=true&download=true oa: '1' project: - _id: '52' name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing' publication: Automatica publication_status: published publisher: Elsevier status: public title: On the Universal Transformation of Data-Driven Models to Control Systems type: journal_article user_id: '47427' volume: 149 year: '2023' ... --- _id: '27426' 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." author: - first_name: Bennet full_name: Gebken, Bennet id: '32643' last_name: Gebken - first_name: Katharina full_name: Bieker, Katharina id: '32829' last_name: Bieker - first_name: Sebastian full_name: Peitz, Sebastian id: '47427' last_name: Peitz orcid: 0000-0002-3389-793X 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 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 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} }' 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.' 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. short: B. Gebken, K. Bieker, S. Peitz, Journal of Global Optimization 85 (2023) 709–741. date_created: 2021-11-15T09:24:59Z date_updated: 2023-03-11T17:16:33Z department: - _id: '101' - _id: '655' doi: 10.1007/s10898-022-01223-2 intvolume: ' 85' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://link.springer.com/content/pdf/10.1007/s10898-022-01223-2.pdf oa: '1' page: 709-741 publication: Journal of Global Optimization status: public title: On the structure of regularization paths for piecewise differentiable regularization terms type: journal_article user_id: '47427' volume: 85 year: '2023' ... --- _id: '20731' 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. article_type: original author: - first_name: Katharina full_name: Bieker, Katharina id: '32829' last_name: Bieker - first_name: Bennet full_name: Gebken, Bennet id: '32643' last_name: Gebken - first_name: Sebastian full_name: Peitz, Sebastian id: '47427' last_name: Peitz orcid: 0000-0002-3389-793X citation: 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 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} }' 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.' 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. short: K. Bieker, B. Gebken, S. Peitz, IEEE Transactions on Pattern Analysis and Machine Intelligence 44 (2022) 7797–7808. date_created: 2020-12-15T07:46:36Z date_updated: 2022-10-21T12:27:16Z ddc: - '510' department: - _id: '101' - _id: '530' - _id: '655' doi: 10.1109/TPAMI.2021.3114962 file: - access_level: closed content_type: application/pdf creator: speitz date_created: 2021-09-25T11:59:15Z date_updated: 2021-09-25T11:59:15Z file_id: '25040' file_name: On_the_Treatment_of_Optimization_Problems_with_L1_Penalty_Terms_via_Multiobjective_Continuation.pdf file_size: 7990831 relation: main_file success: 1 file_date_updated: 2021-09-25T11:59:15Z has_accepted_license: '1' intvolume: ' 44' issue: '11' language: - iso: eng main_file_link: - open_access: '1' url: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9547772 oa: '1' page: 7797-7808 publication: IEEE Transactions on Pattern Analysis and Machine Intelligence publication_status: epub_ahead publisher: IEEE status: public title: On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation type: journal_article user_id: '47427' volume: 44 year: '2022' ... --- _id: '16290' abstract: - lang: eng text: The control of complex systems is of critical importance in many branches of science, engineering, and industry, many of which are governed by nonlinear partial differential equations. Controlling an unsteady fluid flow is particularly important, as flow control is a key enabler for technologies in energy (e.g., wind, tidal, and combustion), transportation (e.g., planes, trains, and automobiles), security (e.g., tracking airborne contamination), and health (e.g., artificial hearts and artificial respiration). However, the high-dimensional, nonlinear, and multi-scale dynamics make real-time feedback control infeasible. Fortunately, these high- dimensional systems exhibit dominant, low-dimensional patterns of activity that can be exploited for effective control in the sense that knowledge of the entire state of a system is not required. Advances in machine learning have the potential to revolutionize flow control given its ability to extract principled, low-rank feature spaces characterizing such complex systems.We present a novel deep learning modelpredictive control framework that exploits low-rank features of the flow in order to achieve considerable improvements to control performance. Instead of predicting the entire fluid state, we use a recurrent neural network (RNN) to accurately predict the control relevant quantities of the system, which are then embedded into an MPC framework to construct a feedback loop. In order to lower the data requirements and to improve the prediction accuracy and thus the control performance, incoming sensor data are used to update the RNN online. The results are validated using varying fluid flow examples of increasing complexity. article_type: original author: - first_name: Katharina full_name: Bieker, Katharina id: '32829' last_name: Bieker - first_name: Sebastian full_name: Peitz, Sebastian id: '47427' last_name: Peitz orcid: https://orcid.org/0000-0002-3389-793X - first_name: Steven L. full_name: Brunton, Steven L. last_name: Brunton - first_name: J. Nathan full_name: Kutz, J. Nathan last_name: Kutz - first_name: Michael full_name: Dellnitz, Michael last_name: Dellnitz citation: ama: Bieker K, Peitz S, Brunton SL, Kutz JN, Dellnitz M. Deep model predictive flow control with limited sensor data and online learning. Theoretical and Computational Fluid Dynamics. 2020;34:577–591. doi:10.1007/s00162-020-00520-4 apa: Bieker, K., Peitz, S., Brunton, S. L., Kutz, J. N., & Dellnitz, M. (2020). Deep model predictive flow control with limited sensor data and online learning. Theoretical and Computational Fluid Dynamics, 34, 577–591. https://doi.org/10.1007/s00162-020-00520-4 bibtex: '@article{Bieker_Peitz_Brunton_Kutz_Dellnitz_2020, title={Deep model predictive flow control with limited sensor data and online learning}, volume={34}, DOI={10.1007/s00162-020-00520-4}, journal={Theoretical and Computational Fluid Dynamics}, author={Bieker, Katharina and Peitz, Sebastian and Brunton, Steven L. and Kutz, J. Nathan and Dellnitz, Michael}, year={2020}, pages={577–591} }' chicago: 'Bieker, Katharina, Sebastian Peitz, Steven L. Brunton, J. Nathan Kutz, and Michael Dellnitz. “Deep Model Predictive Flow Control with Limited Sensor Data and Online Learning.” Theoretical and Computational Fluid Dynamics 34 (2020): 577–591. https://doi.org/10.1007/s00162-020-00520-4.' ieee: K. Bieker, S. Peitz, S. L. Brunton, J. N. Kutz, and M. Dellnitz, “Deep model predictive flow control with limited sensor data and online learning,” Theoretical and Computational Fluid Dynamics, vol. 34, pp. 577–591, 2020. mla: Bieker, Katharina, et al. “Deep Model Predictive Flow Control with Limited Sensor Data and Online Learning.” Theoretical and Computational Fluid Dynamics, vol. 34, 2020, pp. 577–591, doi:10.1007/s00162-020-00520-4. short: K. Bieker, S. Peitz, S.L. Brunton, J.N. Kutz, M. Dellnitz, Theoretical and Computational Fluid Dynamics 34 (2020) 577–591. date_created: 2020-03-13T12:40:09Z date_updated: 2022-01-06T06:52:48Z department: - _id: '101' doi: 10.1007/s00162-020-00520-4 intvolume: ' 34' language: - iso: eng main_file_link: - open_access: '1' url: https://link.springer.com/content/pdf/10.1007/s00162-020-00520-4.pdf oa: '1' page: 577–591 project: - _id: '52' name: Computing Resources Provided by the Paderborn Center for Parallel Computing publication: Theoretical and Computational Fluid Dynamics publication_identifier: issn: - 0935-4964 - 1432-2250 publication_status: published status: public title: Deep model predictive flow control with limited sensor data and online learning type: journal_article user_id: '47427' volume: 34 year: '2020' ...