TY - GEN AU - Mapura Ramirez, Luz Alejandra AU - Kenig, Eugeny Y. ID - 46591 TI - Zur Berechnug von flüssigkeitsseitigen Stoffübergagnskoeffizienten für Strukturpackungen ER - TY - JOUR AB - The Koopman operator has become an essential tool for data-driven approximation of dynamical (control) systems in recent years, e.g., via extended dynamic mode decomposition. Despite its popularity, convergence results and, in particular, error bounds are still quite scarce. In this paper, we derive probabilistic bounds for the approximation error and the prediction error depending on the number of training data points; for both ordinary and stochastic differential equations. Moreover, we extend our analysis to nonlinear control-affine systems using either ergodic trajectories or i.i.d. samples. Here, we exploit the linearity of the Koopman generator to obtain a bilinear system and, thus, circumvent the curse of dimensionality since we do not autonomize the system by augmenting the state by the control inputs. To the best of our knowledge, this is the first finite-data error analysis in the stochastic and/or control setting. Finally, we demonstrate the effectiveness of the proposed approach by comparing it with state-of-the-art techniques showing its superiority whenever state and control are coupled. AU - Nüske, Feliks AU - Peitz, Sebastian AU - Philipp, Friedrich AU - Schaller, Manuel AU - Worthmann, Karl ID - 23428 JF - Journal of Nonlinear Science TI - Finite-data error bounds for Koopman-based prediction and control VL - 33 ER - TY - GEN AB - Different conflicting optimization criteria arise naturally in various Deep Learning scenarios. These can address different main tasks (i.e., in the setting of Multi-Task Learning), but also main and secondary tasks such as loss minimization versus sparsity. The usual approach is a simple weighting of the criteria, which formally only works in the convex setting. In this paper, we present a Multi-Objective Optimization algorithm using a modified Weighted Chebyshev scalarization for training Deep Neural Networks (DNNs) with respect to several tasks. By employing this scalarization technique, the algorithm can identify all optimal solutions of the original problem while reducing its complexity to a sequence of single-objective problems. The simplified problems are then solved using an Augmented Lagrangian method, enabling the use of popular optimization techniques such as Adam and Stochastic Gradient Descent, while efficaciously handling constraints. Our work aims to address the (economical and also ecological) sustainability issue of DNN models, with a particular focus on Deep Multi-Task models, which are typically designed with a very large number of weights to perform equally well on multiple tasks. Through experiments conducted on two Machine Learning datasets, we demonstrate the possibility of adaptively sparsifying the model during training without significantly impacting its performance, if we are willing to apply task-specific adaptations to the network weights. Code is available at https://github.com/salomonhotegni/MDMTN. AU - Hotegni, Sedjro Salomon AU - Peitz, Sebastian AU - Berkemeier, Manuel Bastian ID - 46649 T2 - arXiv:2308.12243 TI - Multi-Objective Optimization for Sparse Deep Neural Network Training ER - TY - JOUR AU - Gonchikzhapov, Munko AU - Kasper, Tina ID - 46637 JF - Applications in Energy and Combustion Science KW - Nanoparticle synthesis KW - Flame spray pyrolysis KW - SpraySyn burner KW - Flame structure KW - Species distribution KW - Temperature distribution SN - 2666-352X TI - Thermal and chemical structure of ethanol and 2-ethylhexanoic acid/ethanol SpraySyn flames VL - 15 ER - TY - JOUR AB - Many problems in science and engineering require an efficient numerical approximation of integrals or solutions to differential equations. For systems with rapidly changing dynamics, an equidistant discretization is often inadvisable as it results in prohibitively large errors or computational effort. To this end, adaptive schemes, such as solvers based on Runge–Kutta pairs, have been developed which adapt the step size based on local error estimations at each step. While the classical schemes apply very generally and are highly efficient on regular systems, they can behave suboptimally when an inefficient step rejection mechanism is triggered by structurally complex systems such as chaotic systems. To overcome these issues, we propose a method to tailor numerical schemes to the problem class at hand. This is achieved by combining simple, classical quadrature rules or ODE solvers with data-driven time-stepping controllers. Compared with learning solution operators to ODEs directly, it generalizes better to unseen initial data as our approach employs classical numerical schemes as base methods. At the same time it can make use of identified structures of a problem class and, therefore, outperforms state-of-the-art adaptive schemes. Several examples demonstrate superior efficiency. Source code is available at https://github.com/lueckem/quadrature-ML. AU - Dellnitz, Michael AU - Hüllermeier, Eyke AU - Lücke, Marvin AU - Ober-Blöbaum, Sina AU - Offen, Christian AU - Peitz, Sebastian AU - Pfannschmidt, Karlson ID - 21600 IS - 2 JF - SIAM Journal on Scientific Computing TI - Efficient time stepping for numerical integration using reinforcement learning VL - 45 ER - TY - CHAP AU - Dahms, Frederik AU - Homberg, Werner ID - 46691 SN - 2195-4356 T2 - Lecture Notes in Mechanical Engineering TI - Analysis and Modelling of the Deformation in the Manufacture of Flange-Contours by the Combined Friction-Spinning and Flow-Forming Process ER - TY - CONF AU - Garnefeld, I. AU - Böhm, Eva AU - Hanf, L. AU - Helm, S. ID - 46665 T2 - 2023 AMA Summer Academic Conference, San Francisco, CA TI - Unboxing video effectiveness – Does speech matter? ER - TY - CONF AU - Kessing, K. AU - Garnefeld, I. AU - Böhm, Eva ID - 46666 T2 - EMAC Annual Conference, Odense, Denmark TI - The dark and bright side of online reviews in manufacturer online shops ER - TY - CONF AU - Hanf, L. AU - Garnefeld, I. AU - Böhm, Eva AU - Helm, S. ID - 46667 T2 - EMAC Annual Conference, Odense, Denmark TI - Stimulating engagement with unboxing videos – Does speech matter? ER - TY - CONF AU - Sadeghi-Kohan, Somayeh AU - Hellebrand, Sybille AU - Wunderlich, Hans-Joachim ID - 46739 T2 - 2023 53rd Annual IEEE/IFIP International Conference on Dependable Systems and Networks Workshops (DSN-W) TI - Low Power Streaming of Sensor Data Using Gray Code-Based Approximate Communication ER -