[{"external_id":{"arxiv":["2411.18422"]},"ddc":["510"],"keyword":["Pareto optimization","Lyapunov analysis","gradient-like dynamical systems","inertial dynamics","asymptotic vanishing damping","Tikhonov regularization","strong convergence"],"language":[{"iso":"eng"}],"publication":"Journal of Mathematical Analysis and Applications","abstract":[{"text":"In this paper we introduce, in a Hilbert space setting, a second order dynamical system with asymptotically vanishing damping and vanishing Tikhonov regularization that approaches a multiobjective optimization problem with convex and differentiable components of the objective function. Trajectory solutions are shown to exist in finite dimensions. We prove fast convergence of the function values, quantified in terms of a merit function. Based on the regime considered, we establish both weak and, in some cases, strong convergence of trajectory solutions toward a weak Pareto optimal solution. To achieve this, we apply Tikhonov regularization individually to each component of the objective function. This work extends results from single objective convex optimization into the multiobjective setting.","lang":"eng"}],"file":[{"file_id":"57473","file_name":"Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization.pdf","access_level":"open_access","file_size":4291134,"creator":"sonntagk","date_created":"2024-11-28T08:58:00Z","date_updated":"2024-11-28T08:58:00Z","relation":"main_file","content_type":"application/pdf"}],"date_created":"2024-11-28T08:58:17Z","title":"Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization","year":"2025","_id":"57472","user_id":"56399","department":[{"_id":"101"},{"_id":"530"},{"_id":"655"}],"file_date_updated":"2024-11-28T08:58:00Z","type":"journal_article","status":"public","oa":"1","date_updated":"2025-10-16T11:56:36Z","author":[{"last_name":"Bot","full_name":"Bot, Radu Ioan","first_name":"Radu Ioan"},{"last_name":"Sonntag","orcid":"https://orcid.org/0000-0003-3384-3496","id":"56399","full_name":"Sonntag, Konstantin","first_name":"Konstantin"}],"main_file_link":[{"url":"https://arxiv.org/pdf/2411.18422"}],"has_accepted_license":"1","citation":{"short":"R.I. Bot, K. Sonntag, Journal of Mathematical Analysis and Applications (2025).","bibtex":"@article{Bot_Sonntag_2025, title={Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization}, journal={Journal of Mathematical Analysis and Applications}, author={Bot, Radu Ioan and Sonntag, Konstantin}, year={2025} }","mla":"Bot, Radu Ioan, and Konstantin Sonntag. “Inertial Dynamics with Vanishing Tikhonov Regularization for Multobjective Optimization.” <i>Journal of Mathematical Analysis and Applications</i>, 2025.","apa":"Bot, R. I., &#38; Sonntag, K. (2025). Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization. <i>Journal of Mathematical Analysis and Applications</i>.","chicago":"Bot, Radu Ioan, and Konstantin Sonntag. “Inertial Dynamics with Vanishing Tikhonov Regularization for Multobjective Optimization.” <i>Journal of Mathematical Analysis and Applications</i>, 2025.","ieee":"R. I. Bot and K. Sonntag, “Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization,” <i>Journal of Mathematical Analysis and Applications</i>, 2025.","ama":"Bot RI, Sonntag K. Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization. <i>Journal of Mathematical Analysis and Applications</i>. Published online 2025."}},{"external_id":{"arxiv":["2402.02494"]},"_id":"51160","user_id":"47427","department":[{"_id":"655"}],"language":[{"iso":"eng"}],"type":"preprint","publication":"arXiv:2402.02494","abstract":[{"lang":"eng","text":"We rigorously derive novel and sharp finite-data error bounds for highly\r\nsample-efficient Extended Dynamic Mode Decomposition (EDMD) for both i.i.d. and\r\nergodic sampling. In particular, we show all results in a very general setting\r\nremoving most of the typically imposed assumptions such that, among others,\r\ndiscrete- and continuous-time stochastic processes as well as nonlinear partial\r\ndifferential equations are contained in the considered system class. Besides\r\nshowing an exponential rate for i.i.d. sampling, we prove, to the best of our\r\nknowledge, the first superlinear convergence rates for ergodic sampling of\r\ndeterministic systems. We verify sharpness of the derived error bounds by\r\nconducting numerical simulations for highly-complex applications from molecular\r\ndynamics and chaotic flame propagation."}],"status":"public","oa":"1","date_updated":"2024-02-06T08:52:44Z","author":[{"first_name":"Friedrich M.","last_name":"Philipp","full_name":"Philipp, Friedrich M."},{"full_name":"Schaller, Manuel","last_name":"Schaller","first_name":"Manuel"},{"last_name":"Boshoff","full_name":"Boshoff, Septimus","first_name":"Septimus"},{"id":"47427","full_name":"Peitz, Sebastian","last_name":"Peitz","orcid":"0000-0002-3389-793X","first_name":"Sebastian"},{"full_name":"Nüske, Feliks","last_name":"Nüske","first_name":"Feliks"},{"last_name":"Worthmann","full_name":"Worthmann, Karl","first_name":"Karl"}],"date_created":"2024-02-06T08:52:21Z","title":"Extended Dynamic Mode Decomposition: Sharp bounds on the sample  efficiency","main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/2402.02494.pdf"}],"year":"2024","citation":{"short":"F.M. Philipp, M. Schaller, S. Boshoff, S. Peitz, F. Nüske, K. Worthmann, ArXiv:2402.02494 (2024).","bibtex":"@article{Philipp_Schaller_Boshoff_Peitz_Nüske_Worthmann_2024, title={Extended Dynamic Mode Decomposition: Sharp bounds on the sample  efficiency}, journal={arXiv:2402.02494}, author={Philipp, Friedrich M. and Schaller, Manuel and Boshoff, Septimus and Peitz, Sebastian and Nüske, Feliks and Worthmann, Karl}, year={2024} }","mla":"Philipp, Friedrich M., et al. “Extended Dynamic Mode Decomposition: Sharp Bounds on the Sample  Efficiency.” <i>ArXiv:2402.02494</i>, 2024.","apa":"Philipp, F. M., Schaller, M., Boshoff, S., Peitz, S., Nüske, F., &#38; Worthmann, K. (2024). Extended Dynamic Mode Decomposition: Sharp bounds on the sample  efficiency. In <i>arXiv:2402.02494</i>.","chicago":"Philipp, Friedrich M., Manuel Schaller, Septimus Boshoff, Sebastian Peitz, Feliks Nüske, and Karl Worthmann. “Extended Dynamic Mode Decomposition: Sharp Bounds on the Sample  Efficiency.” <i>ArXiv:2402.02494</i>, 2024.","ieee":"F. M. Philipp, M. Schaller, S. Boshoff, S. Peitz, F. Nüske, and K. Worthmann, “Extended Dynamic Mode Decomposition: Sharp bounds on the sample  efficiency,” <i>arXiv:2402.02494</i>. 2024.","ama":"Philipp FM, Schaller M, Boshoff S, Peitz S, Nüske F, Worthmann K. Extended Dynamic Mode Decomposition: Sharp bounds on the sample  efficiency. <i>arXiv:240202494</i>. Published online 2024."}},{"department":[{"_id":"101"},{"_id":"655"}],"user_id":"56399","_id":"46019","language":[{"iso":"eng"}],"publication":"Journal of Optimization Theory and Applications","type":"journal_article","status":"public","abstract":[{"lang":"eng","text":"We derive efficient algorithms to compute weakly Pareto optimal solutions for smooth, convex and unconstrained multiobjective optimization problems in general Hilbert spaces. To this end, we define a novel inertial gradient-like dynamical system in the multiobjective setting, which trajectories converge weakly to Pareto optimal solutions. Discretization of this system yields an inertial multiobjective algorithm which generates sequences that converge weakly to Pareto optimal solutions. We employ Nesterov acceleration to define an algorithm with an improved convergence rate compared to the plain multiobjective steepest descent method (Algorithm 1). A further improvement in terms of efficiency is achieved by avoiding the solution of a quadratic subproblem to compute a common step direction for all objective functions, which is usually required in first-order methods. Using a different discretization of our inertial gradient-like dynamical system, we obtain an accelerated multiobjective gradient method that does not require the solution of a subproblem in each step (Algorithm 2). While this algorithm does not converge in general, it yields good results on test problems while being faster than standard steepest descent."}],"author":[{"first_name":"Konstantin","orcid":"https://orcid.org/0000-0003-3384-3496","last_name":"Sonntag","id":"56399","full_name":"Sonntag, Konstantin"},{"orcid":"0000-0002-3389-793X","last_name":"Peitz","full_name":"Peitz, Sebastian","id":"47427","first_name":"Sebastian"}],"date_created":"2023-07-12T06:35:58Z","oa":"1","publisher":"Springer","date_updated":"2024-02-21T10:13:33Z","doi":"10.1007/s10957-024-02389-3","main_file_link":[{"open_access":"1","url":"https://link.springer.com/content/pdf/10.1007/s10957-024-02389-3.pdf"}],"title":"Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems","publication_status":"published","citation":{"chicago":"Sonntag, Konstantin, and Sebastian Peitz. “Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems.” <i>Journal of Optimization Theory and Applications</i>, 2024. <a href=\"https://doi.org/10.1007/s10957-024-02389-3\">https://doi.org/10.1007/s10957-024-02389-3</a>.","ieee":"K. Sonntag and S. Peitz, “Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems,” <i>Journal of Optimization Theory and Applications</i>, 2024, doi: <a href=\"https://doi.org/10.1007/s10957-024-02389-3\">10.1007/s10957-024-02389-3</a>.","ama":"Sonntag K, Peitz S. Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems. <i>Journal of Optimization Theory and Applications</i>. Published online 2024. doi:<a href=\"https://doi.org/10.1007/s10957-024-02389-3\">10.1007/s10957-024-02389-3</a>","short":"K. Sonntag, S. Peitz, Journal of Optimization Theory and Applications (2024).","bibtex":"@article{Sonntag_Peitz_2024, title={Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems}, DOI={<a href=\"https://doi.org/10.1007/s10957-024-02389-3\">10.1007/s10957-024-02389-3</a>}, journal={Journal of Optimization Theory and Applications}, publisher={Springer}, author={Sonntag, Konstantin and Peitz, Sebastian}, year={2024} }","mla":"Sonntag, Konstantin, and Sebastian Peitz. “Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems.” <i>Journal of Optimization Theory and Applications</i>, Springer, 2024, doi:<a href=\"https://doi.org/10.1007/s10957-024-02389-3\">10.1007/s10957-024-02389-3</a>.","apa":"Sonntag, K., &#38; Peitz, S. (2024). Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems. <i>Journal of Optimization Theory and Applications</i>. <a href=\"https://doi.org/10.1007/s10957-024-02389-3\">https://doi.org/10.1007/s10957-024-02389-3</a>"},"year":"2024"},{"type":"preprint","publication":"arXiv:2402.06376","status":"public","abstract":[{"lang":"eng","text":"The efficient optimization method for locally Lipschitz continuous multiobjective optimization problems from [1] is extended from finite-dimensional problems to general Hilbert spaces. The method iteratively computes Pareto critical points, where in each iteration, an approximation of the subdifferential is computed in an efficient manner and then used to compute a common descent direction for all objective functions. To prove convergence, we present some new optimality results for nonsmooth multiobjective optimization problems in Hilbert spaces. Using these, we can show that every accumulation point of the sequence generated by our algorithm is Pareto critical under common assumptions. Computational efficiency for finding Pareto critical points is numerically demonstrated for multiobjective optimal control of an obstacle problem."}],"user_id":"56399","department":[{"_id":"101"},{"_id":"655"}],"external_id":{"arxiv":["\t2402.06376"]},"_id":"51334","language":[{"iso":"eng"}],"has_accepted_license":"1","citation":{"ama":"Sonntag K, Gebken B, Müller G, Peitz S, Volkwein S. A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces. <i>arXiv:240206376</i>. Published online 2024.","chicago":"Sonntag, Konstantin, Bennet Gebken, Georg Müller, Sebastian Peitz, and Stefan Volkwein. “A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces.” <i>ArXiv:2402.06376</i>, 2024.","ieee":"K. Sonntag, B. Gebken, G. Müller, S. Peitz, and S. Volkwein, “A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces,” <i>arXiv:2402.06376</i>. 2024.","apa":"Sonntag, K., Gebken, B., Müller, G., Peitz, S., &#38; Volkwein, S. (2024). A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces. In <i>arXiv:2402.06376</i>.","short":"K. Sonntag, B. Gebken, G. Müller, S. Peitz, S. Volkwein, ArXiv:2402.06376 (2024).","mla":"Sonntag, Konstantin, et al. “A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces.” <i>ArXiv:2402.06376</i>, 2024.","bibtex":"@article{Sonntag_Gebken_Müller_Peitz_Volkwein_2024, title={A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces}, journal={arXiv:2402.06376}, author={Sonntag, Konstantin and Gebken, Bennet and Müller, Georg and Peitz, Sebastian and Volkwein, Stefan}, year={2024} }"},"year":"2024","date_created":"2024-02-13T09:35:26Z","author":[{"orcid":"https://orcid.org/0000-0003-3384-3496","last_name":"Sonntag","id":"56399","full_name":"Sonntag, Konstantin","first_name":"Konstantin"},{"last_name":"Gebken","id":"32643","full_name":"Gebken, Bennet","first_name":"Bennet"},{"first_name":"Georg","full_name":"Müller, Georg","last_name":"Müller"},{"last_name":"Peitz","orcid":"0000-0002-3389-793X","id":"47427","full_name":"Peitz, Sebastian","first_name":"Sebastian"},{"first_name":"Stefan","full_name":"Volkwein, Stefan","last_name":"Volkwein"}],"oa":"1","date_updated":"2024-02-21T10:21:03Z","main_file_link":[{"url":"https://arxiv.org/abs/2402.06376","open_access":"1"}],"title":"A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces"},{"publication":"Physica D: Nonlinear Phenomena","type":"journal_article","status":"public","abstract":[{"text":"We present a convolutional framework which significantly reduces the complexity and thus, the computational effort for distributed reinforcement learning control of dynamical systems governed by partial differential equations (PDEs). Exploiting translational equivariances, the high-dimensional distributed control problem can be transformed into a multi-agent control problem with many identical, uncoupled agents. Furthermore, using the fact that information is transported with finite velocity in many cases, the dimension of the agents’ environment can be drastically reduced using a convolution operation over the state space of the PDE, by which we effectively tackle the curse of dimensionality otherwise present in deep reinforcement learning. In this setting, the complexity can be flexibly adjusted via the kernel width or by using a stride greater than one (meaning that we do not place an actuator at each sensor location). Moreover, scaling from smaller to larger domains – or the transfer between different domains – becomes a straightforward task requiring little effort. We demonstrate the performance of the proposed framework using several PDE examples with increasing complexity, where stabilization is achieved by training a low-dimensional deep deterministic policy gradient agent using minimal computing resources.","lang":"eng"}],"department":[{"_id":"655"}],"user_id":"47427","_id":"40171","language":[{"iso":"eng"}],"article_type":"original","page":"134096","intvolume":"       461","citation":{"apa":"Peitz, S., Stenner, J., Chidananda, V., Wallscheid, O., Brunton, S. L., &#38; Taira, K. (2024). Distributed Control of Partial Differential Equations Using  Convolutional Reinforcement Learning. <i>Physica D: Nonlinear Phenomena</i>, <i>461</i>, 134096. <a href=\"https://doi.org/10.1016/j.physd.2024.134096\">https://doi.org/10.1016/j.physd.2024.134096</a>","mla":"Peitz, Sebastian, et al. “Distributed Control of Partial Differential Equations Using  Convolutional Reinforcement Learning.” <i>Physica D: Nonlinear Phenomena</i>, vol. 461, Elsevier, 2024, p. 134096, doi:<a href=\"https://doi.org/10.1016/j.physd.2024.134096\">10.1016/j.physd.2024.134096</a>.","short":"S. Peitz, J. Stenner, V. Chidananda, O. Wallscheid, S.L. Brunton, K. Taira, Physica D: Nonlinear Phenomena 461 (2024) 134096.","bibtex":"@article{Peitz_Stenner_Chidananda_Wallscheid_Brunton_Taira_2024, title={Distributed Control of Partial Differential Equations Using  Convolutional Reinforcement Learning}, volume={461}, DOI={<a href=\"https://doi.org/10.1016/j.physd.2024.134096\">10.1016/j.physd.2024.134096</a>}, journal={Physica D: Nonlinear Phenomena}, publisher={Elsevier}, author={Peitz, Sebastian and Stenner, Jan and Chidananda, Vikas and Wallscheid, Oliver and Brunton, Steven L. and Taira, Kunihiko}, year={2024}, pages={134096} }","ieee":"S. Peitz, J. Stenner, V. Chidananda, O. Wallscheid, S. L. Brunton, and K. Taira, “Distributed Control of Partial Differential Equations Using  Convolutional Reinforcement Learning,” <i>Physica D: Nonlinear Phenomena</i>, vol. 461, p. 134096, 2024, doi: <a href=\"https://doi.org/10.1016/j.physd.2024.134096\">10.1016/j.physd.2024.134096</a>.","chicago":"Peitz, Sebastian, Jan Stenner, Vikas Chidananda, Oliver Wallscheid, Steven L. Brunton, and Kunihiko Taira. “Distributed Control of Partial Differential Equations Using  Convolutional Reinforcement Learning.” <i>Physica D: Nonlinear Phenomena</i> 461 (2024): 134096. <a href=\"https://doi.org/10.1016/j.physd.2024.134096\">https://doi.org/10.1016/j.physd.2024.134096</a>.","ama":"Peitz S, Stenner J, Chidananda V, Wallscheid O, Brunton SL, Taira K. Distributed Control of Partial Differential Equations Using  Convolutional Reinforcement Learning. <i>Physica D: Nonlinear Phenomena</i>. 2024;461:134096. doi:<a href=\"https://doi.org/10.1016/j.physd.2024.134096\">10.1016/j.physd.2024.134096</a>"},"year":"2024","volume":461,"date_created":"2023-01-26T07:56:26Z","author":[{"last_name":"Peitz","orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian","id":"47427","first_name":"Sebastian"},{"first_name":"Jan","last_name":"Stenner","full_name":"Stenner, Jan","id":"65520"},{"last_name":"Chidananda","full_name":"Chidananda, Vikas","first_name":"Vikas"},{"last_name":"Wallscheid","orcid":"https://orcid.org/0000-0001-9362-8777","id":"11291","full_name":"Wallscheid, Oliver","first_name":"Oliver"},{"full_name":"Brunton, Steven L.","last_name":"Brunton","first_name":"Steven L."},{"full_name":"Taira, Kunihiko","last_name":"Taira","first_name":"Kunihiko"}],"date_updated":"2024-02-23T10:53:42Z","publisher":"Elsevier","oa":"1","doi":"10.1016/j.physd.2024.134096","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1016/j.physd.2024.134096"}],"title":"Distributed Control of Partial Differential Equations Using  Convolutional Reinforcement Learning"},{"title":"Learning Bilinear Models of Actuated Koopman Generators from  Partially-Observed Trajectories","publisher":"SIAM","date_created":"2022-09-22T07:21:40Z","year":"2024","issue":"1","language":[{"iso":"eng"}],"external_id":{"arxiv":["2209.09977"]},"abstract":[{"text":"Data-driven models for nonlinear dynamical systems based on approximating the underlying Koopman operator or generator have proven to be successful tools for forecasting, feature learning, state estimation, and control. It has become well known that the Koopman generators for control-affine systems also have affine dependence on the input, leading to convenient finite-dimensional bilinear approximations of the dynamics. Yet there are still two main obstacles that limit the scope of current approaches for approximating the Koopman generators of systems with actuation. First, the performance of existing methods depends heavily on the choice of basis functions over which the Koopman generator is to be approximated; and there is currently no universal way to choose them for systems that are not measure preserving. Secondly, if we do not observe the full state, we may not gain access to a sufficiently rich collection of such functions to describe the dynamics. This is because the commonly used method of forming time-delayed observables fails when there is actuation. To remedy these issues, we write the dynamics of observables governed by the Koopman generator as a bilinear hidden Markov model, and determine the model parameters using the expectation-maximization (EM) algorithm. The E-step involves a standard Kalman filter and smoother, while the M-step resembles control-affine dynamic mode decomposition for the generator. We demonstrate the performance of this method on three examples, including recovery of a finite-dimensional Koopman-invariant subspace for an actuated system with a slow manifold; estimation of Koopman eigenfunctions for the unforced Duffing equation; and model-predictive control of a fluidic pinball system based only on noisy observations of lift and drag.","lang":"eng"}],"publication":"SIAM Journal on Applied Dynamical Systems","main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/2209.09977.pdf"}],"doi":"10.1137/22M1523601","oa":"1","date_updated":"2024-03-18T10:40:08Z","author":[{"full_name":"Otto, Samuel E.","last_name":"Otto","first_name":"Samuel E."},{"id":"47427","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","last_name":"Peitz","first_name":"Sebastian"},{"first_name":"Clarence W.","full_name":"Rowley, Clarence W.","last_name":"Rowley"}],"volume":23,"citation":{"ieee":"S. E. Otto, S. Peitz, and C. W. Rowley, “Learning Bilinear Models of Actuated Koopman Generators from  Partially-Observed Trajectories,” <i>SIAM Journal on Applied Dynamical Systems</i>, vol. 23, no. 1, pp. 885–923, 2024, doi: <a href=\"https://doi.org/10.1137/22M1523601\">10.1137/22M1523601</a>.","chicago":"Otto, Samuel E., Sebastian Peitz, and Clarence W. Rowley. “Learning Bilinear Models of Actuated Koopman Generators from  Partially-Observed Trajectories.” <i>SIAM Journal on Applied Dynamical Systems</i> 23, no. 1 (2024): 885–923. <a href=\"https://doi.org/10.1137/22M1523601\">https://doi.org/10.1137/22M1523601</a>.","ama":"Otto SE, Peitz S, Rowley CW. Learning Bilinear Models of Actuated Koopman Generators from  Partially-Observed Trajectories. <i>SIAM Journal on Applied Dynamical Systems</i>. 2024;23(1):885-923. doi:<a href=\"https://doi.org/10.1137/22M1523601\">10.1137/22M1523601</a>","apa":"Otto, S. E., Peitz, S., &#38; Rowley, C. W. (2024). Learning Bilinear Models of Actuated Koopman Generators from  Partially-Observed Trajectories. <i>SIAM Journal on Applied Dynamical Systems</i>, <i>23</i>(1), 885–923. <a href=\"https://doi.org/10.1137/22M1523601\">https://doi.org/10.1137/22M1523601</a>","short":"S.E. Otto, S. Peitz, C.W. Rowley, SIAM Journal on Applied Dynamical Systems 23 (2024) 885–923.","mla":"Otto, Samuel E., et al. “Learning Bilinear Models of Actuated Koopman Generators from  Partially-Observed Trajectories.” <i>SIAM Journal on Applied Dynamical Systems</i>, vol. 23, no. 1, SIAM, 2024, pp. 885–923, doi:<a href=\"https://doi.org/10.1137/22M1523601\">10.1137/22M1523601</a>.","bibtex":"@article{Otto_Peitz_Rowley_2024, title={Learning Bilinear Models of Actuated Koopman Generators from  Partially-Observed Trajectories}, volume={23}, DOI={<a href=\"https://doi.org/10.1137/22M1523601\">10.1137/22M1523601</a>}, number={1}, journal={SIAM Journal on Applied Dynamical Systems}, publisher={SIAM}, author={Otto, Samuel E. and Peitz, Sebastian and Rowley, Clarence W.}, year={2024}, pages={885–923} }"},"intvolume":"        23","page":"885-923","publication_status":"published","project":[{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"_id":"33461","user_id":"47427","department":[{"_id":"655"}],"status":"public","type":"journal_article"},{"publisher":"Springer ","date_created":"2023-01-23T07:03:39Z","title":"Error bounds for kernel-based approximations of the Koopman operator","year":"2024","external_id":{"arxiv":["2301.08637"]},"language":[{"iso":"eng"}],"publication":"Applied and Computational Harmonic Analysis ","abstract":[{"text":"We consider the data-driven approximation of the Koopman operator for\r\nstochastic differential equations on reproducing kernel Hilbert spaces (RKHS).\r\nOur focus is on the estimation error if the data are collected from long-term\r\nergodic simulations. We derive both an exact expression for the variance of the\r\nkernel cross-covariance operator, measured in the Hilbert-Schmidt norm, and\r\nprobabilistic bounds for the finite-data estimation error. Moreover, we derive\r\na bound on the prediction error of observables in the RKHS using a finite\r\nMercer series expansion. Further, assuming Koopman-invariance of the RKHS, we\r\nprovide bounds on the full approximation error. Numerical experiments using the\r\nOrnstein-Uhlenbeck process illustrate our results.","lang":"eng"}],"oa":"1","date_updated":"2024-04-11T12:41:13Z","volume":71,"author":[{"first_name":"Friedrich","full_name":"Philipp, Friedrich","last_name":"Philipp"},{"last_name":"Schaller","full_name":"Schaller, Manuel","first_name":"Manuel"},{"first_name":"Karl","full_name":"Worthmann, Karl","last_name":"Worthmann"},{"first_name":"Sebastian","orcid":"0000-0002-3389-793X","last_name":"Peitz","id":"47427","full_name":"Peitz, Sebastian"},{"first_name":"Feliks","full_name":"Nüske, Feliks","last_name":"Nüske"}],"doi":"10.1016/j.acha.2024.101657","main_file_link":[{"url":"https://arxiv.org/pdf/2301.08637","open_access":"1"}],"publication_status":"published","intvolume":"        71","citation":{"ama":"Philipp F, Schaller M, Worthmann K, Peitz S, Nüske F. Error bounds for kernel-based approximations of the Koopman operator. <i>Applied and Computational Harmonic Analysis </i>. 2024;71. doi:<a href=\"https://doi.org/10.1016/j.acha.2024.101657\">10.1016/j.acha.2024.101657</a>","chicago":"Philipp, Friedrich, Manuel Schaller, Karl Worthmann, Sebastian Peitz, and Feliks Nüske. “Error Bounds for Kernel-Based Approximations of the Koopman Operator.” <i>Applied and Computational Harmonic Analysis </i> 71 (2024). <a href=\"https://doi.org/10.1016/j.acha.2024.101657\">https://doi.org/10.1016/j.acha.2024.101657</a>.","ieee":"F. Philipp, M. Schaller, K. Worthmann, S. Peitz, and F. Nüske, “Error bounds for kernel-based approximations of the Koopman operator,” <i>Applied and Computational Harmonic Analysis </i>, vol. 71, Art. no. 101657, 2024, doi: <a href=\"https://doi.org/10.1016/j.acha.2024.101657\">10.1016/j.acha.2024.101657</a>.","short":"F. Philipp, M. Schaller, K. Worthmann, S. Peitz, F. Nüske, Applied and Computational Harmonic Analysis  71 (2024).","bibtex":"@article{Philipp_Schaller_Worthmann_Peitz_Nüske_2024, title={Error bounds for kernel-based approximations of the Koopman operator}, volume={71}, DOI={<a href=\"https://doi.org/10.1016/j.acha.2024.101657\">10.1016/j.acha.2024.101657</a>}, number={101657}, journal={Applied and Computational Harmonic Analysis }, publisher={Springer }, author={Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl and Peitz, Sebastian and Nüske, Feliks}, year={2024} }","mla":"Philipp, Friedrich, et al. “Error Bounds for Kernel-Based Approximations of the Koopman Operator.” <i>Applied and Computational Harmonic Analysis </i>, vol. 71, 101657, Springer , 2024, doi:<a href=\"https://doi.org/10.1016/j.acha.2024.101657\">10.1016/j.acha.2024.101657</a>.","apa":"Philipp, F., Schaller, M., Worthmann, K., Peitz, S., &#38; Nüske, F. (2024). Error bounds for kernel-based approximations of the Koopman operator. <i>Applied and Computational Harmonic Analysis </i>, <i>71</i>, Article 101657. <a href=\"https://doi.org/10.1016/j.acha.2024.101657\">https://doi.org/10.1016/j.acha.2024.101657</a>"},"_id":"38031","department":[{"_id":"655"}],"user_id":"47427","article_number":"101657","type":"journal_article","status":"public"},{"citation":{"ama":"Akhter J, Fährmann PD, Sonntag K, Peitz S. Common pitfalls to avoid while using multiobjective optimization in machine learning. <i>arXiv</i>. Published online 2024.","chicago":"Akhter, Junaid, Paul David Fährmann, Konstantin Sonntag, and Sebastian Peitz. “Common Pitfalls to Avoid While Using Multiobjective Optimization in Machine Learning.” <i>ArXiv</i>, 2024.","ieee":"J. Akhter, P. D. Fährmann, K. Sonntag, and S. Peitz, “Common pitfalls to avoid while using multiobjective optimization in machine learning,” <i>arXiv</i>. 2024.","apa":"Akhter, J., Fährmann, P. D., Sonntag, K., &#38; Peitz, S. (2024). Common pitfalls to avoid while using multiobjective optimization in machine learning. In <i>arXiv</i>.","short":"J. Akhter, P.D. Fährmann, K. Sonntag, S. Peitz, ArXiv (2024).","bibtex":"@article{Akhter_Fährmann_Sonntag_Peitz_2024, title={Common pitfalls to avoid while using multiobjective optimization in machine learning}, journal={arXiv}, author={Akhter, Junaid and Fährmann, Paul David and Sonntag, Konstantin and Peitz, Sebastian}, year={2024} }","mla":"Akhter, Junaid, et al. “Common Pitfalls to Avoid While Using Multiobjective Optimization in Machine Learning.” <i>ArXiv</i>, 2024."},"year":"2024","date_created":"2024-05-03T13:38:34Z","author":[{"last_name":"Akhter","full_name":"Akhter, Junaid","id":"97994","first_name":"Junaid"},{"last_name":"Fährmann","full_name":"Fährmann, Paul David","first_name":"Paul David"},{"last_name":"Sonntag","orcid":"https://orcid.org/0000-0003-3384-3496","full_name":"Sonntag, Konstantin","id":"56399","first_name":"Konstantin"},{"full_name":"Peitz, Sebastian","id":"47427","last_name":"Peitz","orcid":"0000-0002-3389-793X","first_name":"Sebastian"}],"date_updated":"2024-05-06T08:29:38Z","oa":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/2405.01480"}],"title":"Common pitfalls to avoid while using multiobjective optimization in machine learning","type":"preprint","publication":"arXiv","status":"public","user_id":"47427","department":[{"_id":"655"}],"_id":"53858","language":[{"iso":"eng"}]},{"volume":34,"date_created":"2022-07-28T11:53:02Z","author":[{"orcid":"https://orcid.org/0000-0003-3384-3496","last_name":"Sonntag","full_name":"Sonntag, Konstantin","id":"56399","first_name":"Konstantin"},{"orcid":"0000-0002-3389-793X","last_name":"Peitz","id":"47427","full_name":"Peitz, Sebastian","first_name":"Sebastian"}],"publisher":"Society for Industrial and Applied Mathematics","date_updated":"2024-07-02T09:27:39Z","doi":"10.1137/23M1588512","title":"Fast Convergence of Inertial Multiobjective Gradient-Like Systems with Asymptotic Vanishing Damping","issue":"3","publication_identifier":{"issn":["1095-7189"]},"publication_status":"published","page":"2259 - 2286","intvolume":"        34","citation":{"ieee":"K. Sonntag and S. Peitz, “Fast Convergence of Inertial Multiobjective Gradient-Like Systems with Asymptotic Vanishing Damping,” <i>SIAM Journal on Optimization</i>, vol. 34, no. 3, pp. 2259–2286, 2024, doi: <a href=\"https://doi.org/10.1137/23M1588512\">10.1137/23M1588512</a>.","chicago":"Sonntag, Konstantin, and Sebastian Peitz. “Fast Convergence of Inertial Multiobjective Gradient-Like Systems with Asymptotic Vanishing Damping.” <i>SIAM Journal on Optimization</i> 34, no. 3 (2024): 2259–86. <a href=\"https://doi.org/10.1137/23M1588512\">https://doi.org/10.1137/23M1588512</a>.","apa":"Sonntag, K., &#38; Peitz, S. (2024). Fast Convergence of Inertial Multiobjective Gradient-Like Systems with Asymptotic Vanishing Damping. <i>SIAM Journal on Optimization</i>, <i>34</i>(3), 2259–2286. <a href=\"https://doi.org/10.1137/23M1588512\">https://doi.org/10.1137/23M1588512</a>","ama":"Sonntag K, Peitz S. Fast Convergence of Inertial Multiobjective Gradient-Like Systems with Asymptotic Vanishing Damping. <i>SIAM Journal on Optimization</i>. 2024;34(3):2259-2286. doi:<a href=\"https://doi.org/10.1137/23M1588512\">10.1137/23M1588512</a>","mla":"Sonntag, Konstantin, and Sebastian Peitz. “Fast Convergence of Inertial Multiobjective Gradient-Like Systems with Asymptotic Vanishing Damping.” <i>SIAM Journal on Optimization</i>, vol. 34, no. 3, Society for Industrial and Applied Mathematics, 2024, pp. 2259–86, doi:<a href=\"https://doi.org/10.1137/23M1588512\">10.1137/23M1588512</a>.","short":"K. Sonntag, S. Peitz, SIAM Journal on Optimization 34 (2024) 2259–2286.","bibtex":"@article{Sonntag_Peitz_2024, title={Fast Convergence of Inertial Multiobjective Gradient-Like Systems with Asymptotic Vanishing Damping}, volume={34}, DOI={<a href=\"https://doi.org/10.1137/23M1588512\">10.1137/23M1588512</a>}, number={3}, journal={SIAM Journal on Optimization}, publisher={Society for Industrial and Applied Mathematics}, author={Sonntag, Konstantin and Peitz, Sebastian}, year={2024}, pages={2259–2286} }"},"year":"2024","department":[{"_id":"101"},{"_id":"655"}],"user_id":"56399","_id":"32447","language":[{"iso":"eng"}],"keyword":["multiobjective optimization","Pareto optimization","Lyapunov analysis","gradient-likedynamical systems","inertial dynamics","asymptotic vanishing damping","fast convergence"],"article_type":"original","publication":"SIAM Journal on Optimization","type":"journal_article","status":"public","abstract":[{"text":"We present a new gradient-like dynamical system related to unconstrained convex smooth multiobjective optimization which involves inertial effects and asymptotic vanishing damping. To the best of our knowledge, this system is the first inertial gradient-like system for multiobjective optimization problems including asymptotic vanishing damping, expanding the ideas previously laid out in [H. Attouch and G. Garrigos, Multiobjective Optimization: An Inertial Dynamical Approach to Pareto Optima, preprint, arXiv:1506.02823, 2015]. We prove existence of solutions to this system in finite dimensions and further prove that its bounded solutions converge weakly to weakly Pareto optimal points. In addition, we obtain a convergence rate of order \\(\\mathcal{O}(t^{-2})\\) for the function values measured with a merit function. This approach presents a good basis for the development of fast gradient methods for multiobjective optimization.","lang":"eng"}]},{"publication_status":"published","publication_identifier":{"eisbn":["979-8-3503-5931-2"],"eissn":[" 2161-4407"]},"has_accepted_license":"1","citation":{"ama":"Hotegni SS, Berkemeier MB, Peitz S. Multi-Objective Optimization for Sparse Deep Multi-Task Learning. In: <i>2024 International Joint Conference on Neural Networks (IJCNN)</i>. IEEE; 2024:9. doi:<a href=\"https://doi.org/10.1109/IJCNN60899.2024.10650994\">10.1109/IJCNN60899.2024.10650994</a>","chicago":"Hotegni, Sedjro Salomon, Manuel Bastian Berkemeier, and Sebastian Peitz. “Multi-Objective Optimization for Sparse Deep Multi-Task Learning.” In <i>2024 International Joint Conference on Neural Networks (IJCNN)</i>, 9. Yokohama, Japan: IEEE, 2024. <a href=\"https://doi.org/10.1109/IJCNN60899.2024.10650994\">https://doi.org/10.1109/IJCNN60899.2024.10650994</a>.","ieee":"S. S. Hotegni, M. B. Berkemeier, and S. Peitz, “Multi-Objective Optimization for Sparse Deep Multi-Task Learning,” in <i>2024 International Joint Conference on Neural Networks (IJCNN)</i>, Yokohama, Japan, 2024, p. 9, doi: <a href=\"https://doi.org/10.1109/IJCNN60899.2024.10650994\">10.1109/IJCNN60899.2024.10650994</a>.","short":"S.S. Hotegni, M.B. Berkemeier, S. Peitz, in: 2024 International Joint Conference on Neural Networks (IJCNN), IEEE, Yokohama, Japan, 2024, p. 9.","bibtex":"@inproceedings{Hotegni_Berkemeier_Peitz_2024, place={Yokohama, Japan}, title={Multi-Objective Optimization for Sparse Deep Multi-Task Learning}, DOI={<a href=\"https://doi.org/10.1109/IJCNN60899.2024.10650994\">10.1109/IJCNN60899.2024.10650994</a>}, booktitle={2024 International Joint Conference on Neural Networks (IJCNN)}, publisher={IEEE}, author={Hotegni, Sedjro Salomon and Berkemeier, Manuel Bastian and Peitz, Sebastian}, year={2024}, pages={9} }","mla":"Hotegni, Sedjro Salomon, et al. “Multi-Objective Optimization for Sparse Deep Multi-Task Learning.” <i>2024 International Joint Conference on Neural Networks (IJCNN)</i>, IEEE, 2024, p. 9, doi:<a href=\"https://doi.org/10.1109/IJCNN60899.2024.10650994\">10.1109/IJCNN60899.2024.10650994</a>.","apa":"Hotegni, S. S., Berkemeier, M. B., &#38; Peitz, S. (2024). Multi-Objective Optimization for Sparse Deep Multi-Task Learning. <i>2024 International Joint Conference on Neural Networks (IJCNN)</i>, 9. <a href=\"https://doi.org/10.1109/IJCNN60899.2024.10650994\">https://doi.org/10.1109/IJCNN60899.2024.10650994</a>"},"page":"9","place":"Yokohama, Japan","author":[{"full_name":"Hotegni, Sedjro Salomon","id":"97995","last_name":"Hotegni","first_name":"Sedjro Salomon"},{"last_name":"Berkemeier","id":"51701","full_name":"Berkemeier, Manuel Bastian","first_name":"Manuel Bastian"},{"full_name":"Peitz, Sebastian","id":"47427","last_name":"Peitz","orcid":"0000-0002-3389-793X","first_name":"Sebastian"}],"date_updated":"2024-09-27T10:24:22Z","oa":"1","main_file_link":[{"open_access":"1","url":"https://ieeexplore.ieee.org/document/10650994"}],"doi":"10.1109/IJCNN60899.2024.10650994","conference":{"start_date":"2024-06-30","name":"2024 International Joint Conference on Neural Networks (IJCNN)","location":"Yokohama, Japan","end_date":"2024-07-05"},"type":"conference","status":"public","user_id":"97995","department":[{"_id":"655"}],"_id":"46649","year":"2024","date_created":"2023-08-24T07:44:36Z","publisher":"IEEE","title":"Multi-Objective Optimization for Sparse Deep Multi-Task Learning","publication":"2024 International Joint Conference on Neural Networks (IJCNN)","abstract":[{"text":"Different conflicting optimization criteria arise naturally in various Deep\r\nLearning scenarios. These can address different main tasks (i.e., in the\r\nsetting of Multi-Task Learning), but also main and secondary tasks such as loss\r\nminimization versus sparsity. The usual approach is a simple weighting of the\r\ncriteria, which formally only works in the convex setting. In this paper, we\r\npresent a Multi-Objective Optimization algorithm using a modified Weighted\r\nChebyshev scalarization for training Deep Neural Networks (DNNs) with respect\r\nto several tasks. By employing this scalarization technique, the algorithm can\r\nidentify all optimal solutions of the original problem while reducing its\r\ncomplexity to a sequence of single-objective problems. The simplified problems\r\nare then solved using an Augmented Lagrangian method, enabling the use of\r\npopular optimization techniques such as Adam and Stochastic Gradient Descent,\r\nwhile efficaciously handling constraints. Our work aims to address the\r\n(economical and also ecological) sustainability issue of DNN models, with a\r\nparticular focus on Deep Multi-Task models, which are typically designed with a\r\nvery large number of weights to perform equally well on multiple tasks. Through\r\nexperiments conducted on two Machine Learning datasets, we demonstrate the\r\npossibility of adaptively sparsifying the model during training without\r\nsignificantly impacting its performance, if we are willing to apply\r\ntask-specific adaptations to the network weights. Code is available at\r\nhttps://github.com/salomonhotegni/MDMTN.","lang":"eng"}],"language":[{"iso":"eng"}]},{"language":[{"iso":"eng"}],"article_number":"110840","department":[{"_id":"101"},{"_id":"655"}],"user_id":"47427","_id":"21199","project":[{"_id":"52","name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"status":"public","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."}],"publication":"Automatica","type":"journal_article","doi":"10.1016/j.automatica.2022.110840","main_file_link":[{"open_access":"1","url":"https://www.sciencedirect.com/science/article/pii/S0005109822007075/pdfft?isDTMRedir=true&download=true"}],"title":"On the Universal Transformation of Data-Driven Models to Control Systems","volume":149,"author":[{"id":"47427","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","last_name":"Peitz","first_name":"Sebastian"},{"first_name":"Katharina","id":"32829","full_name":"Bieker, Katharina","last_name":"Bieker"}],"date_created":"2021-02-10T07:04:15Z","oa":"1","date_updated":"2023-01-07T12:01:58Z","publisher":"Elsevier","intvolume":"       149","citation":{"ama":"Peitz S, Bieker K. On the Universal Transformation of Data-Driven Models to Control Systems. <i>Automatica</i>. 2023;149. doi:<a href=\"https://doi.org/10.1016/j.automatica.2022.110840\">10.1016/j.automatica.2022.110840</a>","chicago":"Peitz, Sebastian, and Katharina Bieker. “On the Universal Transformation of Data-Driven Models to Control Systems.” <i>Automatica</i> 149 (2023). <a href=\"https://doi.org/10.1016/j.automatica.2022.110840\">https://doi.org/10.1016/j.automatica.2022.110840</a>.","ieee":"S. Peitz and K. Bieker, “On the Universal Transformation of Data-Driven Models to Control Systems,” <i>Automatica</i>, vol. 149, Art. no. 110840, 2023, doi: <a href=\"https://doi.org/10.1016/j.automatica.2022.110840\">10.1016/j.automatica.2022.110840</a>.","apa":"Peitz, S., &#38; Bieker, K. (2023). On the Universal Transformation of Data-Driven Models to Control Systems. <i>Automatica</i>, <i>149</i>, Article 110840. <a href=\"https://doi.org/10.1016/j.automatica.2022.110840\">https://doi.org/10.1016/j.automatica.2022.110840</a>","short":"S. Peitz, K. Bieker, Automatica 149 (2023).","mla":"Peitz, Sebastian, and Katharina Bieker. “On the Universal Transformation of Data-Driven Models to Control Systems.” <i>Automatica</i>, vol. 149, 110840, Elsevier, 2023, doi:<a href=\"https://doi.org/10.1016/j.automatica.2022.110840\">10.1016/j.automatica.2022.110840</a>.","bibtex":"@article{Peitz_Bieker_2023, title={On the Universal Transformation of Data-Driven Models to Control Systems}, volume={149}, DOI={<a href=\"https://doi.org/10.1016/j.automatica.2022.110840\">10.1016/j.automatica.2022.110840</a>}, number={110840}, journal={Automatica}, publisher={Elsevier}, author={Peitz, Sebastian and Bieker, Katharina}, year={2023} }"},"year":"2023","publication_status":"published"},{"language":[{"iso":"eng"}],"user_id":"47427","department":[{"_id":"655"},{"_id":"623"}],"_id":"48502","status":"public","abstract":[{"text":"The prediction of photon echoes is an important technique for gaining an understanding of optical quantum systems. However, this requires a large number of simulations with varying parameters and/or input pulses, which renders numerical studies expensive. This article investigates how we can use data-driven surrogate models based on the Koopman operator to accelerate this process. In order to be successful, we require a model that is accurate over a large number of time steps. To this end, we employ a bilinear Koopman model using extended dynamic mode decomposition and simulate the optical Bloch equations for an ensemble of inhomogeneously broadened two-level systems. Such systems are well suited to describe the excitation of excitonic resonances in semiconductor nanostructures, for example, ensembles of semiconductor quantum dots. We perform a detailed study on the required number of system simulations such that the resulting data-driven Koopman model is sufficiently accurate for a wide range of parameter settings. We analyze the L2 error and the relative error of the photon echo peak and investigate how the control positions relate to the stabilization. After proper training, the dynamics of the quantum ensemble can be predicted accurately and numerically very efficiently by our methods.","lang":"eng"}],"type":"preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/2310.16578.pdf"}],"title":"Accelerating the analysis of optical quantum systems using the Koopman operator","author":[{"last_name":"Peitz","orcid":"0000-0002-3389-793X","id":"47427","full_name":"Peitz, Sebastian","first_name":"Sebastian"},{"full_name":"Hunstig, Anna","last_name":"Hunstig","first_name":"Anna"},{"last_name":"Rose","orcid":"0000-0002-3079-5428","full_name":"Rose, Hendrik","id":"55958","first_name":"Hendrik"},{"id":"344","full_name":"Meier, Torsten","orcid":"0000-0001-8864-2072","last_name":"Meier","first_name":"Torsten"}],"date_created":"2023-10-27T09:40:59Z","date_updated":"2023-10-27T10:05:07Z","oa":"1","citation":{"ieee":"S. Peitz, A. Hunstig, H. Rose, and T. Meier, “Accelerating the analysis of optical quantum systems using the Koopman operator.” 2023.","chicago":"Peitz, Sebastian, Anna Hunstig, Hendrik Rose, and Torsten Meier. “Accelerating the Analysis of Optical Quantum Systems Using the Koopman Operator,” 2023.","ama":"Peitz S, Hunstig A, Rose H, Meier T. Accelerating the analysis of optical quantum systems using the Koopman operator. Published online 2023.","short":"S. Peitz, A. Hunstig, H. Rose, T. Meier, (2023).","bibtex":"@article{Peitz_Hunstig_Rose_Meier_2023, title={Accelerating the analysis of optical quantum systems using the Koopman operator}, author={Peitz, Sebastian and Hunstig, Anna and Rose, Hendrik and Meier, Torsten}, year={2023} }","mla":"Peitz, Sebastian, et al. <i>Accelerating the Analysis of Optical Quantum Systems Using the Koopman Operator</i>. 2023.","apa":"Peitz, S., Hunstig, A., Rose, H., &#38; Meier, T. (2023). <i>Accelerating the analysis of optical quantum systems using the Koopman operator</i>."},"year":"2023"},{"type":"preprint","publication":"arXiv","status":"public","abstract":[{"text":"Sparsity is a highly desired feature in deep neural networks (DNNs) since it ensures numerical efficiency, improves the interpretability of models (due to the smaller number of relevant features), and robustness. In machine learning approaches based on linear models, it is well known that there exists a connecting path between the sparsest solution in terms of the $\\ell^1$ norm,i.e., zero weights and the non-regularized solution, which is called the regularization path. Very recently, there was a first attempt to extend the concept of regularization paths to DNNs by means of treating the empirical loss and sparsity ($\\ell^1$ norm) as two conflicting criteria and solving the resulting multiobjective optimization problem. However, due to the non-smoothness of the $\\ell^1$ norm and the high number of parameters, this approach is not very efficient from a computational perspective. To overcome this limitation, we present an algorithm that allows for the approximation of the entire Pareto front for the above-mentioned objectives in a very efficient manner. We present numerical examples using both deterministic and stochastic gradients. We furthermore demonstrate that knowledge of the regularization path allows for a well-generalizing network parametrization.","lang":"eng"}],"user_id":"47427","department":[{"_id":"655"}],"_id":"51159","language":[{"iso":"eng"}],"citation":{"ama":"Amakor AC, Sonntag K, Peitz S. A multiobjective continuation method to compute the regularization path of deep neural networks. <i>arXiv</i>. Published online 2023.","chicago":"Amakor, Augustina Chidinma, Konstantin Sonntag, and Sebastian Peitz. “A Multiobjective Continuation Method to Compute the Regularization Path of Deep Neural Networks.” <i>ArXiv</i>, 2023.","ieee":"A. C. Amakor, K. Sonntag, and S. Peitz, “A multiobjective continuation method to compute the regularization path of deep neural networks,” <i>arXiv</i>. 2023.","apa":"Amakor, A. C., Sonntag, K., &#38; Peitz, S. (2023). A multiobjective continuation method to compute the regularization path of deep neural networks. In <i>arXiv</i>.","mla":"Amakor, Augustina Chidinma, et al. “A Multiobjective Continuation Method to Compute the Regularization Path of Deep Neural Networks.” <i>ArXiv</i>, 2023.","short":"A.C. Amakor, K. Sonntag, S. Peitz, ArXiv (2023).","bibtex":"@article{Amakor_Sonntag_Peitz_2023, title={A multiobjective continuation method to compute the regularization path of deep neural networks}, journal={arXiv}, author={Amakor, Augustina Chidinma and Sonntag, Konstantin and Peitz, Sebastian}, year={2023} }"},"year":"2023","date_created":"2024-02-06T08:51:00Z","author":[{"full_name":"Amakor, Augustina Chidinma","id":"97916","last_name":"Amakor","first_name":"Augustina Chidinma"},{"id":"56399","full_name":"Sonntag, Konstantin","last_name":"Sonntag","first_name":"Konstantin"},{"first_name":"Sebastian","last_name":"Peitz","orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian","id":"47427"}],"oa":"1","date_updated":"2024-02-06T08:52:07Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/2308.12044.pdf"}],"title":"A multiobjective continuation method to compute the regularization path of deep neural networks"},{"status":"public","abstract":[{"lang":"eng","text":"Extended Dynamic Mode Decomposition (EDMD) is a popular data-driven method to\r\napproximate the Koopman operator for deterministic and stochastic (control)\r\nsystems. This operator is linear and encompasses full information on the\r\n(expected stochastic) dynamics. In this paper, we analyze a kernel-based EDMD\r\nalgorithm, known as kEDMD, where the dictionary consists of the canonical\r\nkernel features at the data points. The latter are acquired by i.i.d. samples\r\nfrom a user-defined and application-driven distribution on a compact set. We\r\nprove bounds on the prediction error of the kEDMD estimator when sampling from\r\nthis (not necessarily ergodic) distribution. The error analysis is further\r\nextended to control-affine systems, where the considered invariance of the\r\nReproducing Kernel Hilbert Space is significantly less restrictive in\r\ncomparison to invariance assumptions on an a-priori chosen dictionary."}],"publication":"arXiv:2312.10460","type":"preprint","language":[{"iso":"eng"}],"department":[{"_id":"655"}],"user_id":"47427","_id":"51158","external_id":{"arxiv":["2312.10460"]},"citation":{"ama":"Philipp F, Schaller M, Worthmann K, Peitz S, Nüske F. Error analysis of kernel EDMD for prediction and control in the Koopman  framework. <i>arXiv:231210460</i>. Published online 2023.","chicago":"Philipp, Friedrich, Manuel Schaller, Karl Worthmann, Sebastian Peitz, and Feliks Nüske. “Error Analysis of Kernel EDMD for Prediction and Control in the Koopman  Framework.” <i>ArXiv:2312.10460</i>, 2023.","ieee":"F. Philipp, M. Schaller, K. Worthmann, S. Peitz, and F. Nüske, “Error analysis of kernel EDMD for prediction and control in the Koopman  framework,” <i>arXiv:2312.10460</i>. 2023.","apa":"Philipp, F., Schaller, M., Worthmann, K., Peitz, S., &#38; Nüske, F. (2023). Error analysis of kernel EDMD for prediction and control in the Koopman  framework. In <i>arXiv:2312.10460</i>.","short":"F. Philipp, M. Schaller, K. Worthmann, S. Peitz, F. Nüske, ArXiv:2312.10460 (2023).","mla":"Philipp, Friedrich, et al. “Error Analysis of Kernel EDMD for Prediction and Control in the Koopman  Framework.” <i>ArXiv:2312.10460</i>, 2023.","bibtex":"@article{Philipp_Schaller_Worthmann_Peitz_Nüske_2023, title={Error analysis of kernel EDMD for prediction and control in the Koopman  framework}, journal={arXiv:2312.10460}, author={Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl and Peitz, Sebastian and Nüske, Feliks}, year={2023} }"},"year":"2023","main_file_link":[{"url":"https://arxiv.org/pdf/2312.10460.pdf","open_access":"1"}],"title":"Error analysis of kernel EDMD for prediction and control in the Koopman  framework","author":[{"last_name":"Philipp","full_name":"Philipp, Friedrich","first_name":"Friedrich"},{"full_name":"Schaller, Manuel","last_name":"Schaller","first_name":"Manuel"},{"first_name":"Karl","last_name":"Worthmann","full_name":"Worthmann, Karl"},{"id":"47427","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","last_name":"Peitz","first_name":"Sebastian"},{"full_name":"Nüske, Feliks","last_name":"Nüske","first_name":"Feliks"}],"date_created":"2024-02-06T08:49:50Z","oa":"1","date_updated":"2024-02-06T08:50:32Z"},{"oa":"1","date_updated":"2024-02-21T12:22:20Z","date_created":"2023-08-21T05:50:12Z","author":[{"first_name":"Marco","last_name":"Bernreuther","full_name":"Bernreuther, Marco"},{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"},{"full_name":"Gebken, Bennet","id":"32643","last_name":"Gebken","first_name":"Bennet"},{"first_name":"Georg","last_name":"Müller","full_name":"Müller, Georg"},{"first_name":"Sebastian","full_name":"Peitz, Sebastian","id":"47427","last_name":"Peitz","orcid":"0000-0002-3389-793X"},{"first_name":"Konstantin","last_name":"Sonntag","orcid":"https://orcid.org/0000-0003-3384-3496","full_name":"Sonntag, Konstantin","id":"56399"},{"first_name":"Stefan","full_name":"Volkwein, Stefan","last_name":"Volkwein"}],"title":"Multiobjective Optimization of Non-Smooth PDE-Constrained Problems","main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/2308.01113"}],"year":"2023","citation":{"chicago":"Bernreuther, Marco, Michael Dellnitz, Bennet Gebken, Georg Müller, Sebastian Peitz, Konstantin Sonntag, and Stefan Volkwein. “Multiobjective Optimization of Non-Smooth PDE-Constrained Problems.” <i>ArXiv:2308.01113</i>, 2023.","ieee":"M. Bernreuther <i>et al.</i>, “Multiobjective Optimization of Non-Smooth PDE-Constrained Problems,” <i>arXiv:2308.01113</i>. 2023.","ama":"Bernreuther M, Dellnitz M, Gebken B, et al. Multiobjective Optimization of Non-Smooth PDE-Constrained Problems. <i>arXiv:230801113</i>. Published online 2023.","apa":"Bernreuther, M., Dellnitz, M., Gebken, B., Müller, G., Peitz, S., Sonntag, K., &#38; Volkwein, S. (2023). Multiobjective Optimization of Non-Smooth PDE-Constrained Problems. In <i>arXiv:2308.01113</i>.","mla":"Bernreuther, Marco, et al. “Multiobjective Optimization of Non-Smooth PDE-Constrained Problems.” <i>ArXiv:2308.01113</i>, 2023.","short":"M. Bernreuther, M. Dellnitz, B. Gebken, G. Müller, S. Peitz, K. Sonntag, S. Volkwein, ArXiv:2308.01113 (2023).","bibtex":"@article{Bernreuther_Dellnitz_Gebken_Müller_Peitz_Sonntag_Volkwein_2023, title={Multiobjective Optimization of Non-Smooth PDE-Constrained Problems}, journal={arXiv:2308.01113}, author={Bernreuther, Marco and Dellnitz, Michael and Gebken, Bennet and Müller, Georg and Peitz, Sebastian and Sonntag, Konstantin and Volkwein, Stefan}, year={2023} }"},"_id":"46578","external_id":{"arxiv":["2308.01113"]},"department":[{"_id":"655"},{"_id":"101"}],"user_id":"47427","language":[{"iso":"eng"}],"publication":"arXiv:2308.01113","type":"preprint","abstract":[{"lang":"eng","text":"Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control - potentially with non-smoothness both on the level of the objectives or in the system dynamics. This results in new challenges such as dealing with expensive models (e.g., governed by partial differential equations (PDEs)) and developing dedicated algorithms handling the non-smoothness. Since in contrast to single-objective optimization, the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in the field of multiobjective optimization of non-smooth PDE-constrained problems. In particular we report on the advances achieved within Project 2 \"Multiobjective Optimization of Non-Smooth PDE-Constrained Problems - Switches, State Constraints and Model Order Reduction\" of the DFG Priority Programm 1962 \"Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization\"."}],"status":"public"},{"publication_identifier":{"isbn":["978-3-8007-6318-4"]},"year":"2023","citation":{"ama":"Boshoff S, Stenner J, Weber D, et al. Hybrid control of interconnected power converters using both expert-driven droop and data-driven reinforcement learning approaches. In: <i>IEEE Power and Energy Student Summit (PESS)</i>. VDE; 2023:124-129.","chicago":"Boshoff, Septimus, Jan Stenner, Daniel Weber, Marvin Meyer, Vikas Chidananda, Sebastian Peitz, and Oliver Wallscheid. “Hybrid Control of Interconnected Power Converters Using Both Expert-Driven Droop and Data-Driven Reinforcement Learning Approaches.” In <i>IEEE Power and Energy Student Summit (PESS)</i>, 124–29. VDE, 2023.","ieee":"S. Boshoff <i>et al.</i>, “Hybrid control of interconnected power converters using both expert-driven droop and data-driven reinforcement learning approaches,” in <i>IEEE Power and Energy Student Summit (PESS)</i>, 2023, pp. 124–129.","apa":"Boshoff, S., Stenner, J., Weber, D., Meyer, M., Chidananda, V., Peitz, S., &#38; Wallscheid, O. (2023). Hybrid control of interconnected power converters using both expert-driven droop and data-driven reinforcement learning approaches. <i>IEEE Power and Energy Student Summit (PESS)</i>, 124–129.","bibtex":"@inproceedings{Boshoff_Stenner_Weber_Meyer_Chidananda_Peitz_Wallscheid_2023, title={Hybrid control of interconnected power converters using both expert-driven droop and data-driven reinforcement learning approaches}, booktitle={IEEE Power and Energy Student Summit (PESS)}, publisher={VDE}, author={Boshoff, Septimus and Stenner, Jan and Weber, Daniel and Meyer, Marvin and Chidananda, Vikas and Peitz, Sebastian and Wallscheid, Oliver}, year={2023}, pages={124–129} }","short":"S. Boshoff, J. Stenner, D. Weber, M. Meyer, V. Chidananda, S. Peitz, O. Wallscheid, in: IEEE Power and Energy Student Summit (PESS), VDE, 2023, pp. 124–129.","mla":"Boshoff, Septimus, et al. “Hybrid Control of Interconnected Power Converters Using Both Expert-Driven Droop and Data-Driven Reinforcement Learning Approaches.” <i>IEEE Power and Energy Student Summit (PESS)</i>, VDE, 2023, pp. 124–29."},"page":"124-129","publisher":"VDE","date_updated":"2024-06-21T08:28:45Z","author":[{"first_name":"Septimus","full_name":"Boshoff, Septimus","last_name":"Boshoff"},{"full_name":"Stenner, Jan","id":"65520","last_name":"Stenner","first_name":"Jan"},{"full_name":"Weber, Daniel","id":"24041","orcid":"0000-0003-3367-5998","last_name":"Weber","first_name":"Daniel"},{"last_name":"Meyer","full_name":"Meyer, Marvin","first_name":"Marvin"},{"first_name":"Vikas","full_name":"Chidananda, Vikas","last_name":"Chidananda"},{"orcid":"0000-0002-3389-793X","last_name":"Peitz","id":"47427","full_name":"Peitz, Sebastian","first_name":"Sebastian"},{"full_name":"Wallscheid, Oliver","id":"11291","last_name":"Wallscheid","orcid":"https://orcid.org/0000-0001-9362-8777","first_name":"Oliver"}],"date_created":"2024-06-21T07:12:10Z","title":"Hybrid control of interconnected power converters using both expert-driven droop and data-driven reinforcement learning approaches","main_file_link":[{"url":"https://ieeexplore.ieee.org/document/10564542"}],"type":"conference","publication":"IEEE Power and Energy Student Summit (PESS)","status":"public","project":[{"name":"DARE: DARE: Trainings-, Validierungs- und Benchmarkwerkzeuge zur Entwicklung datengetriebener Betriebs- und Regelungsverfahren für intelligente, lokale Energiesysteme","_id":"286","grant_number":"01IS20164"}],"_id":"54838","user_id":"47427","department":[{"_id":"655"},{"_id":"52"}],"language":[{"iso":"eng"}]},{"status":"public","publication":"IEEE Power and Energy Student Summit (PESS)","type":"conference","language":[{"iso":"eng"}],"_id":"54839","project":[{"name":"DARE: DARE: Trainings-, Validierungs- und Benchmarkwerkzeuge zur Entwicklung datengetriebener Betriebs- und Regelungsverfahren für intelligente, lokale Energiesysteme","_id":"286","grant_number":"01IS20164"}],"department":[{"_id":"655"},{"_id":"52"}],"user_id":"47427","year":"2023","page":"112-117","citation":{"chicago":"Meyer, Marvin, Daniel Weber, Vikas Chidananda, Oliver Schweins, Jan Stenner, Septimus Boshoff, Sebastian Peitz, and Oliver Wallscheid. “ElectricGrid.Jl – Automated Modeling of Decentralized Electrical Energy Grids.” In <i>IEEE Power and Energy Student Summit (PESS)</i>, 112–17. VDE, 2023.","ieee":"M. Meyer <i>et al.</i>, “ElectricGrid.jl – Automated modeling of decentralized electrical energy grids,” in <i>IEEE Power and Energy Student Summit (PESS)</i>, 2023, pp. 112–117.","ama":"Meyer M, Weber D, Chidananda V, et al. ElectricGrid.jl – Automated modeling of decentralized electrical energy grids. In: <i>IEEE Power and Energy Student Summit (PESS)</i>. VDE; 2023:112-117.","apa":"Meyer, M., Weber, D., Chidananda, V., Schweins, O., Stenner, J., Boshoff, S., Peitz, S., &#38; Wallscheid, O. (2023). ElectricGrid.jl – Automated modeling of decentralized electrical energy grids. <i>IEEE Power and Energy Student Summit (PESS)</i>, 112–117.","bibtex":"@inproceedings{Meyer_Weber_Chidananda_Schweins_Stenner_Boshoff_Peitz_Wallscheid_2023, title={ElectricGrid.jl – Automated modeling of decentralized electrical energy grids}, booktitle={IEEE Power and Energy Student Summit (PESS)}, publisher={VDE}, author={Meyer, Marvin and Weber, Daniel and Chidananda, Vikas and Schweins, Oliver and Stenner, Jan and Boshoff, Septimus and Peitz, Sebastian and Wallscheid, Oliver}, year={2023}, pages={112–117} }","short":"M. Meyer, D. Weber, V. Chidananda, O. Schweins, J. Stenner, S. Boshoff, S. Peitz, O. Wallscheid, in: IEEE Power and Energy Student Summit (PESS), VDE, 2023, pp. 112–117.","mla":"Meyer, Marvin, et al. “ElectricGrid.Jl – Automated Modeling of Decentralized Electrical Energy Grids.” <i>IEEE Power and Energy Student Summit (PESS)</i>, VDE, 2023, pp. 112–17."},"publication_identifier":{"isbn":["978-3-8007-6318-4"]},"title":"ElectricGrid.jl – Automated modeling of decentralized electrical energy grids","main_file_link":[{"url":"https://ieeexplore.ieee.org/document/10564557"}],"date_updated":"2024-06-21T08:28:35Z","publisher":"VDE","date_created":"2024-06-21T07:13:11Z","author":[{"first_name":"Marvin","last_name":"Meyer","full_name":"Meyer, Marvin"},{"last_name":"Weber","orcid":"0000-0003-3367-5998","full_name":"Weber, Daniel","id":"24041","first_name":"Daniel"},{"full_name":"Chidananda, Vikas","last_name":"Chidananda","first_name":"Vikas"},{"last_name":"Schweins","full_name":"Schweins, Oliver","first_name":"Oliver"},{"first_name":"Jan","last_name":"Stenner","id":"65520","full_name":"Stenner, Jan"},{"first_name":"Septimus","full_name":"Boshoff, Septimus","last_name":"Boshoff"},{"first_name":"Sebastian","last_name":"Peitz","orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian","id":"47427"},{"last_name":"Wallscheid","orcid":"https://orcid.org/0000-0001-9362-8777","full_name":"Wallscheid, Oliver","id":"11291","first_name":"Oliver"}]},{"abstract":[{"lang":"eng","text":"The goal of this paper is to make a strong point for the usage of dynamical models when using reinforcement learning (RL) for feedback control of dynamical systems governed by partial differential equations (PDEs). To breach the gap between the immense promises we see in RL and the applicability in complex engineering systems, the main challenges are the massive requirements in terms of the training data, as well as the lack of performance guarantees. We present a solution for the first issue using a data-driven surrogate model in the form of a convolutional LSTM with actuation. We demonstrate that learning an actuated model in parallel to training the RL agent significantly reduces the total amount of required data sampled from the real system. Furthermore, we show that iteratively updating the model is of major importance to avoid biases in the RL training. Detailed ablation studies reveal the most important ingredients of the modeling process. We use the chaotic Kuramoto-Sivashinsky equation do demonstarte our findings."}],"status":"public","type":"preprint","publication":"arXiv:2302.07160","language":[{"iso":"eng"}],"external_id":{"arxiv":["2302.07160"]},"_id":"42160","user_id":"47427","department":[{"_id":"655"}],"year":"2023","citation":{"apa":"Werner, S., &#38; Peitz, S. (2023). Learning a model is paramount for sample efficiency in reinforcement  learning control of PDEs. In <i>arXiv:2302.07160</i>.","bibtex":"@article{Werner_Peitz_2023, title={Learning a model is paramount for sample efficiency in reinforcement  learning control of PDEs}, journal={arXiv:2302.07160}, author={Werner, Stefan and Peitz, Sebastian}, year={2023} }","mla":"Werner, Stefan, and Sebastian Peitz. “Learning a Model Is Paramount for Sample Efficiency in Reinforcement  Learning Control of PDEs.” <i>ArXiv:2302.07160</i>, 2023.","short":"S. Werner, S. Peitz, ArXiv:2302.07160 (2023).","ama":"Werner S, Peitz S. Learning a model is paramount for sample efficiency in reinforcement  learning control of PDEs. <i>arXiv:230207160</i>. Published online 2023.","ieee":"S. Werner and S. Peitz, “Learning a model is paramount for sample efficiency in reinforcement  learning control of PDEs,” <i>arXiv:2302.07160</i>. 2023.","chicago":"Werner, Stefan, and Sebastian Peitz. “Learning a Model Is Paramount for Sample Efficiency in Reinforcement  Learning Control of PDEs.” <i>ArXiv:2302.07160</i>, 2023."},"title":"Learning a model is paramount for sample efficiency in reinforcement  learning control of PDEs","main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/2302.07160"}],"date_updated":"2023-02-15T20:58:33Z","oa":"1","author":[{"first_name":"Stefan","full_name":"Werner, Stefan","last_name":"Werner"},{"first_name":"Sebastian","full_name":"Peitz, Sebastian","id":"47427","last_name":"Peitz","orcid":"0000-0002-3389-793X"}],"date_created":"2023-02-15T20:57:20Z"},{"abstract":[{"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.","lang":"eng"}],"status":"public","type":"journal_article","publication":"Journal of Global Optimization","language":[{"iso":"eng"}],"_id":"27426","user_id":"47427","department":[{"_id":"101"},{"_id":"655"}],"year":"2023","citation":{"ama":"Gebken B, Bieker K, Peitz S. On the structure of regularization paths for piecewise differentiable regularization terms. <i>Journal of Global Optimization</i>. 2023;85(3):709-741. doi:<a href=\"https://doi.org/10.1007/s10898-022-01223-2\">10.1007/s10898-022-01223-2</a>","ieee":"B. Gebken, K. Bieker, and S. Peitz, “On the structure of regularization paths for piecewise differentiable regularization terms,” <i>Journal of Global Optimization</i>, vol. 85, no. 3, pp. 709–741, 2023, doi: <a href=\"https://doi.org/10.1007/s10898-022-01223-2\">10.1007/s10898-022-01223-2</a>.","chicago":"Gebken, Bennet, Katharina Bieker, and Sebastian Peitz. “On the Structure of Regularization Paths for Piecewise Differentiable Regularization Terms.” <i>Journal of Global Optimization</i> 85, no. 3 (2023): 709–41. <a href=\"https://doi.org/10.1007/s10898-022-01223-2\">https://doi.org/10.1007/s10898-022-01223-2</a>.","apa":"Gebken, B., Bieker, K., &#38; Peitz, S. (2023). On the structure of regularization paths for piecewise differentiable regularization terms. <i>Journal of Global Optimization</i>, <i>85</i>(3), 709–741. <a href=\"https://doi.org/10.1007/s10898-022-01223-2\">https://doi.org/10.1007/s10898-022-01223-2</a>","mla":"Gebken, Bennet, et al. “On the Structure of Regularization Paths for Piecewise Differentiable Regularization Terms.” <i>Journal of Global Optimization</i>, vol. 85, no. 3, 2023, pp. 709–41, doi:<a href=\"https://doi.org/10.1007/s10898-022-01223-2\">10.1007/s10898-022-01223-2</a>.","bibtex":"@article{Gebken_Bieker_Peitz_2023, title={On the structure of regularization paths for piecewise differentiable regularization terms}, volume={85}, DOI={<a href=\"https://doi.org/10.1007/s10898-022-01223-2\">10.1007/s10898-022-01223-2</a>}, 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."},"page":"709-741","intvolume":"        85","issue":"3","title":"On the structure of regularization paths for piecewise differentiable regularization terms","main_file_link":[{"url":"https://link.springer.com/content/pdf/10.1007/s10898-022-01223-2.pdf","open_access":"1"}],"doi":"10.1007/s10898-022-01223-2","oa":"1","date_updated":"2023-03-11T17:16:33Z","author":[{"id":"32643","full_name":"Gebken, Bennet","last_name":"Gebken","first_name":"Bennet"},{"first_name":"Katharina","id":"32829","full_name":"Bieker, Katharina","last_name":"Bieker"},{"first_name":"Sebastian","last_name":"Peitz","orcid":"0000-0002-3389-793X","id":"47427","full_name":"Peitz, Sebastian"}],"date_created":"2021-11-15T09:24:59Z","volume":85},{"year":"2023","issue":"1","title":"Towards reliable data-based optimal and predictive control using extended DMD","date_created":"2022-02-25T17:14:58Z","abstract":[{"lang":"eng","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."}],"publication":"IFAC-PapersOnLine","language":[{"iso":"eng"}],"external_id":{"arxiv":["2202.09084"]},"intvolume":"        56","page":"169-174","citation":{"ieee":"M. Schaller, K. Worthmann, F. Philipp, S. Peitz, and F. Nüske, “Towards reliable data-based optimal and predictive control using extended DMD,” in <i>IFAC-PapersOnLine</i>, 2023, vol. 56, no. 1, pp. 169–174, doi: <a href=\"https://doi.org/10.1016/j.ifacol.2023.02.029\">10.1016/j.ifacol.2023.02.029</a>.","chicago":"Schaller, Manuel, Karl Worthmann, Friedrich Philipp, Sebastian Peitz, and Feliks Nüske. “Towards Reliable Data-Based Optimal and Predictive Control Using Extended DMD.” In <i>IFAC-PapersOnLine</i>, 56:169–74, 2023. <a href=\"https://doi.org/10.1016/j.ifacol.2023.02.029\">https://doi.org/10.1016/j.ifacol.2023.02.029</a>.","ama":"Schaller M, Worthmann K, Philipp F, Peitz S, Nüske F. Towards reliable data-based optimal and predictive control using extended DMD. In: <i>IFAC-PapersOnLine</i>. Vol 56. ; 2023:169-174. doi:<a href=\"https://doi.org/10.1016/j.ifacol.2023.02.029\">10.1016/j.ifacol.2023.02.029</a>","mla":"Schaller, Manuel, et al. “Towards Reliable Data-Based Optimal and Predictive Control Using Extended DMD.” <i>IFAC-PapersOnLine</i>, vol. 56, no. 1, 2023, pp. 169–74, doi:<a href=\"https://doi.org/10.1016/j.ifacol.2023.02.029\">10.1016/j.ifacol.2023.02.029</a>.","bibtex":"@inproceedings{Schaller_Worthmann_Philipp_Peitz_Nüske_2023, title={Towards reliable data-based optimal and predictive control using extended DMD}, volume={56}, DOI={<a href=\"https://doi.org/10.1016/j.ifacol.2023.02.029\">10.1016/j.ifacol.2023.02.029</a>}, 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., &#38; Nüske, F. (2023). Towards reliable data-based optimal and predictive control using extended DMD. <i>IFAC-PapersOnLine</i>, <i>56</i>(1), 169–174. <a href=\"https://doi.org/10.1016/j.ifacol.2023.02.029\">https://doi.org/10.1016/j.ifacol.2023.02.029</a>"},"publication_status":"published","conference":{"name":"12th IFAC Symposium on Nonlinear Control Systems (NOLCOS)"},"doi":"10.1016/j.ifacol.2023.02.029","main_file_link":[{"open_access":"1","url":"https://www.sciencedirect.com/science/article/pii/S2405896323002173/pdf?md5=164ee9a0343a1bd0e0b9ac4187e44b77&pid=1-s2.0-S2405896323002173-main.pdf"}],"date_updated":"2023-03-17T15:55:33Z","oa":"1","volume":56,"author":[{"first_name":"Manuel","full_name":"Schaller, Manuel","last_name":"Schaller"},{"first_name":"Karl","full_name":"Worthmann, Karl","last_name":"Worthmann"},{"last_name":"Philipp","full_name":"Philipp, Friedrich","first_name":"Friedrich"},{"last_name":"Peitz","orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian","id":"47427","first_name":"Sebastian"},{"first_name":"Feliks","last_name":"Nüske","orcid":"0000-0003-2444-7889","full_name":"Nüske, Feliks","id":"81513"}],"status":"public","type":"conference","_id":"30125","department":[{"_id":"655"}],"user_id":"47427"}]