@article{51160, abstract = {{We rigorously derive novel and sharp finite-data error bounds for highly sample-efficient Extended Dynamic Mode Decomposition (EDMD) for both i.i.d. and ergodic sampling. In particular, we show all results in a very general setting removing most of the typically imposed assumptions such that, among others, discrete- and continuous-time stochastic processes as well as nonlinear partial differential equations are contained in the considered system class. Besides showing an exponential rate for i.i.d. sampling, we prove, to the best of our knowledge, the first superlinear convergence rates for ergodic sampling of deterministic systems. We verify sharpness of the derived error bounds by conducting numerical simulations for highly-complex applications from molecular dynamics and chaotic flame propagation.}}, author = {{Philipp, Friedrich M. and Schaller, Manuel and Boshoff, Septimus and Peitz, Sebastian and Nüske, Feliks and Worthmann, Karl}}, journal = {{Physica D: Nonlinear Phenomena}}, title = {{{Variance representations and convergence rates for data-driven approximations of Koopman operators}}}, doi = {{10.1016/j.physd.2026.135223}}, volume = {{492}}, year = {{2026}}, } @article{53858, author = {{Akhter, Junaid and Fährmann, Paul David and Sonntag, Konstantin and Peitz, Sebastian}}, journal = {{SIAM Review}}, number = {{3}}, pages = {{656--683}}, publisher = {{SIAM}}, title = {{{Common pitfalls to avoid while using multiobjective optimization in machine learning}}}, doi = {{10.1137/24M1658875}}, volume = {{68}}, year = {{2026}}, } @inproceedings{67308, abstract = {{Optimizing large-scale multibody systems is a challenging task, particularly in the presence of multiple conflicting criteria. To prevent high simulation costs, surrogate models constructed from a small number of expensive model evaluations are very popular. However, it is difficult to ensure the optimality of the obtained solutions using a single pre-computed model. We present a back-and-forth approach between surrogate modeling and multi-objective optimization, and we compare different strategies for optimization, sampling, and surrogate modeling, to identify the most promising approach in terms of computational efficiency and solution quality.}}, author = {{Amakor, Augustina Chidinma and Berkemeier, Manuel B. and Wohlleben, Meike Claudia and Sextro, Walter and Peitz, Sebastian}}, booktitle = {{Artificial Neural Networks and Machine Learning – ICANN 2025}}, editor = {{Senn, Walter and Sanguineti, Marcello and Saudargiene, Ausra and Tetko, Igor V. and Villa, Alessandro E. P. and Jirsa, Viktor and Bengio, Yoshua}}, isbn = {{978-3-032-04555-3}}, keywords = {{own, own-conference}}, pages = {{251–262}}, publisher = {{Springer Nature Switzerland}}, title = {{{Surrogate-Assisted Multi-objective Design of Complex Multibody Systems}}}, doi = {{10.1007/978-3-032-04555-3_21}}, year = {{2026}}, } @inproceedings{67307, author = {{Hotegni, Sedjro Salomon and Peitz, Sebastian}}, booktitle = {{14th International Conference on Learning Representations (ICLR)}}, keywords = {{own, own-conference}}, title = {{{SPREAD: Sampling-based Pareto front Refinement via Efficient Adaptive Diffusion}}}, doi = {{10.48550/arXiv.2509.21058}}, year = {{2026}}, } @unpublished{67306, author = {{Stenner, Jan and Harder, Hans and Peitz, Sebastian}}, booktitle = {{arXiv:2606.30238}}, keywords = {{own, own-preprint, erc}}, title = {{{Sparse Sensor Placement in Multi-Agent Reinforcement Learning Control of Rayleigh-Bénard Convection}}}, year = {{2026}}, } @unpublished{67309, author = {{Stenner, Jan and Kilian, Alexander and Peitz, Sebastian and de Meer, Hermann}}, booktitle = {{arXiv:2606.30316}}, keywords = {{own, own-preprint}}, title = {{{Toward an Energy-Optimized Operation of Data Centers Located in Wind Farms Using Reinforcement Learning}}}, year = {{2026}}, } @inproceedings{67300, abstract = {{Deep neural networks (DNNs) are vulnerable to small adversarial perturbations, which are tiny changes to the input data that appear insignificant but cause the model to produce drastically different outputs. Many defense methods require modifying model architectures during evaluation or performing test-time data purification. This not only introduces additional complexity but is often architecture-dependent. We show, however, that robust feature learning during training can significantly enhance DNN robustness. We propose MOREL, a multi-objective approach that aligns natural and adversarial features using cosine similarity and multi-positive contrastive losses to encourage similar features for same-class inputs. Extensive experiments demonstrate that MOREL significantly improves robustness against both white-box and black-box attacks. Our code is available at https://github.com/salomonhotegni/MOREL.}}, author = {{Hotegni, Sedjro Salomon and Peitz, Sebastian}}, booktitle = {{Artificial Neural Networks and Machine Learning – ICANN 2025}}, editor = {{Senn, Walter and Sanguineti, Marcello and Saudargiene, Ausra and Tetko, Igor V. and Villa, Alessandro E. P. and Jirsa, Viktor and Bengio, Yoshua}}, isbn = {{978-3-032-04558-4}}, keywords = {{own, own-conference}}, pages = {{442–454}}, publisher = {{Springer Nature Switzerland}}, title = {{{Enhancing Adversarial Robustness Through Multi-objective Representation Learning}}}, doi = {{10.1007/978-3-032-04558-4_35}}, year = {{2026}}, } @article{67302, abstract = {{Data-driven surrogate models provide fast and fully differentiable approximations of complex dynamical systems. In this work, we develop such surrogates for the Rayleigh–Bénard convection (RBC), which governs thermally driven flows in natural and industrial environments. Specifically, the proposed models approximate the discrete-time flow map of the RBC system, advancing the full system state by a fixed time step. We train Fourier Neural Operator (FNO)–based models to learn the dynamics of RBC in two and three dimensions and compare them to a convolutional U-Net baseline and a Koopman-based Linear Recurrent Autoencoder Network (LRAN). The two-dimensional system serves as a baseline for the more challenging three-dimensional case, which exhibits increased spatial complexity and turbulent dynamics. Across all settings, FNO-based models consistently outperform the LRAN, while achieving performance comparable to the U-Net in several regimes. Incorporating spatio-temporal inputs via FNOs leads to improved long-term prediction accuracy, particularly for turbulent flows. The physical fidelity of the predictions is assessed using convective heat flux statistics, profiles, and fluctuations, showing that FNOs most closely reproduce the ground-truth flow statistics. In addition, we demonstrate that FNOs enable zero-shot super-resolution across unseen spatial discretizations, a capability not shared by the convolutional baselines. These results highlight the potential of neural operator–based models as accurate, physically consistent, and resolution-independent surrogates for downstream tasks such as flow control.}}, author = {{Markmann, Thorben and Straat, Michiel and Peitz, Sebastian and Hammer, Barbara}}, issn = {{0925-2312}}, journal = {{Neurocomputing}}, keywords = {{own, own-journal, erc}}, pages = {{133201}}, title = {{{Fourier neural operators as data-driven surrogates for two- and three-dimensional Rayleigh–Bénard convection}}}, doi = {{10.1016/j.neucom.2026.133201}}, volume = {{679}}, year = {{2026}}, } @inproceedings{67299, author = {{Harder, Hans and Vishwasrao, Abhijeet and Guastoni, Luca and Vinuesa, Ricardo and Peitz, Sebastian}}, booktitle = {{Proceedings of The 8th Annual Learning for Dynamics and Control Conference}}, editor = {{Sukhatme, Gaurav and Lindemann, Lars and Tu, Stephen and Wierman, Adam and Atanasov, Nikolay}}, keywords = {{own, own-conference, erc}}, pages = {{1601–1619}}, publisher = {{PMLR}}, title = {{{Efficient probabilistic surrogate modeling techniques for partially-observed large-scale dynamical systems}}}, doi = {{10.48550/arXiv.2511.04641}}, volume = {{331}}, year = {{2026}}, } @inproceedings{67303, author = {{Amakor, Augustina Chidinma and Sonntag, Konstantin and Peitz, Sebastian}}, booktitle = {{European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD)}}, keywords = {{own, own-conference}}, pages = {{652--668}}, title = {{{Interactive Pareto navigation for deep multi-task learning}}}, doi = {{10.1007/978-3-032-37667-1_37}}, year = {{2026}}, } @inproceedings{67305, author = {{Becktepe, Jannis and Franz, Aleksandra and Thuerey, Nils and Peitz, Sebastian}}, booktitle = {{International Conference on Machine Learning (ICML)}}, keywords = {{own, own-conference, erc}}, title = {{{Plug-and-Play Benchmarking of Reinforcement Learning Algorithms for Large-Scale Flow Control}}}, doi = {{10.48550/arXiv.2601.15015}}, year = {{2026}}, } @article{67301, author = {{Wohlleben, Meike Claudia and Schütte, Jan and Berkemeier, Manuel and Sextro, Walter and Peitz, Sebastian}}, journal = {{Multibody System Dynamics}}, keywords = {{own, own-journal}}, title = {{{Evaluating Physics-Based, Hybrid, and Data-Driven Models for Rubber-Metal Bushings}}}, doi = {{10.1007/s11044-026-10146-9}}, year = {{2026}}, } @unpublished{67298, author = {{Mugisho Zagabe, Christian and Peitz, Sebastian}}, booktitle = {{arXiv:2603.26464}}, keywords = {{own, own-preprint, erc}}, title = {{{Automatic feature identification in least-squares policy iteration using the Koopman operator framework}}}, year = {{2026}}, } @unpublished{67304, author = {{Plotzki, Tim and Peitz, Sebastian}}, booktitle = {{arXiv:2603.28074}}, keywords = {{own, own-preprint, erc}}, title = {{{Koopman-based surrogate modeling for reinforcement-learning-control of Rayleigh-Benard convection}}}, year = {{2026}}, } @article{51159, abstract = {{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.}}, author = {{Amakor, Augustina Chidinma and Sonntag, Konstantin and Peitz, Sebastian}}, journal = {{Machine Learning with Applications}}, publisher = {{Elsevier}}, title = {{{A multiobjective continuation method to compute the regularization path of deep neural networks}}}, doi = {{10.1016/j.mlwa.2025.100625}}, volume = {{19}}, year = {{2025}}, } @article{46579, abstract = {{The Koopman operator has become an essential tool for data-driven analysis, prediction and control of complex systems, the main reason being the enormous potential of identifying linear function space representations of nonlinear dynamics from measurements. Until now, the situation where for large-scale systems, we (i) only have access to partial observations (i.e., measurements, as is very common for experimental data) or (ii) deliberately perform coarse graining (for efficiency reasons) has not been treated to its full extent. In this paper, we address the pitfall associated with this situation, that the classical EDMD algorithm does not automatically provide a Koopman operator approximation for the underlying system if we do not carefully select the number of observables. Moreover, we show that symmetries in the system dynamics can be carried over to the Koopman operator, which allows us to massively increase the model efficiency. We also briefly draw a connection to domain decomposition techniques for partial differential equations and present numerical evidence using the Kuramoto--Sivashinsky equation.}}, author = {{Peitz, Sebastian and Harder, Hans and Nüske, Feliks and Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl}}, journal = {{Journal of Computational Dynamics}}, pages = {{305--324}}, title = {{{Equivariance and partial observations in Koopman operator theory for partial differential equations}}}, doi = {{10.3934/jcd.2024035}}, volume = {{12}}, year = {{2025}}, } @inproceedings{53793, abstract = {{We utilize extreme learning machines for the prediction of partial differential equations (PDEs). Our method splits the state space into multiple windows that are predicted individually using a single model. Despite requiring only few data points (in some cases, our method can learn from a single full-state snapshot), it still achieves high accuracy and can predict the flow of PDEs over long time horizons. Moreover, we show how additional symmetries can be exploited to increase sample efficiency and to enforce equivariance.}}, author = {{Harder, Hans and Peitz, Sebastian}}, booktitle = {{Systems theory in data and optimization}}, editor = {{Berberich, J. and Ianelli, A. and Allgöwer, F.}}, isbn = {{978-3-031-83191-1}}, keywords = {{extreme learning machines, partial differential equations, data-driven prediction, high-dimensional systems}}, pages = {{153--168}}, publisher = {{Springer}}, title = {{{Solving partial differential equations with equivariant extreme learning machines}}}, doi = {{10.1007/978-3-031-83191-1_10}}, year = {{2025}}, } @inproceedings{67313, author = {{Voth, Diana and Dane, Leonidas and Grebe, Jonas and Peitz, Sebastian and Terhörst, Philipp}}, booktitle = {{2025 IEEE/CVF Winter Conference on Applications of Computer Vision (WACV)}}, keywords = {{own, own-conference}}, pages = {{1027--1039}}, title = {{{Effective Backdoor Learning on Open-Set Face Recognition Systems}}}, doi = {{10.1109/WACV61041.2025.00109}}, year = {{2025}}, } @unpublished{67312, author = {{Markmann, Thorben and Straat, Michiel and Peitz, Sebastian and Hammer, Barbara}}, booktitle = {{arXiv:2504.12000}}, keywords = {{own, own-preprint}}, title = {{{Control of Rayleigh-Bénard Convection: Effectiveness of Reinforcement Learning in the Turbulent Regime}}}, year = {{2025}}, } @unpublished{67310, author = {{Boshoff, Septimus and Peitz, Sebastian and Klus, Stefan}}, booktitle = {{arXiv:2509.22482}}, keywords = {{own, own-preprint}}, title = {{{Bayesian Transfer Operators in Reproducing Kernel Hilbert Spaces}}}, year = {{2025}}, }