TY - JOUR A1 - Bouanani, Hafida A1 - Kebiri, Omar A1 - Hartmann, Carsten A1 - Redjil, Amel T1 - Optimal Relaxed Control for a Decoupled G-FBSDE JF - Journal of Optimization Theory and Applications N2 - AbstractIn this paper we study a system of decoupled forward-backward stochastic differential equations driven by a G-Brownian motion (G-FBSDEs) with non-degenerate diffusion. Our objective is to establish the existence of a relaxed optimal control for a non-smooth stochastic optimal control problem. The latter is given in terms of a decoupled G-FBSDE. The cost functional is the solution of the backward stochastic differential equation at the initial time. The key idea to establish existence of a relaxed optimal control is to replace the original control problem by a suitably regularised problem with mollified coefficients, prove the existence of a relaxed control, and then pass to the limit. Y1 - 2024 U6 - https://doi.org/10.1007/s10957-024-02495-2 SN - 0022-3239 VL - 202 IS - 3 SP - 1027 EP - 1059 PB - Springer Science and Business Media LLC ER - TY - CHAP A1 - Hartmann, Carsten A1 - Richter, Lorenz ED - Klimczak, Peter ED - Petersen, Christer T1 - Transgressing the boundaries: towards a rigorous understanding of deep learning and its (non-)robustness T2 - Artificial Intelligence – Limits and Prospects Y1 - 2023 SN - 978-3-8376-5732-6 U6 - https://doi.org/10.14361/9783839457320-004 SP - 43 EP - 82 PB - transcript Verlag CY - Bielefeld ER - TY - GEN A1 - Schütte, Christof A1 - Klus, Stefan A1 - Hartmann, Carsten T1 - Overcoming the Timescale Barrier in Molecular Dynamics: Transfer Operators, Variational Principles, and Machine Learning T2 - Acta Numerica Y1 - 2023 U6 - https://doi.org/10.1017/S0962492923000016 SN - 1474-0508 SN - 0962-4929 VL - Vol. 32 SP - 517 EP - 673 ER - TY - GEN A1 - Mansouri Yarahmadi, Ashkan A1 - Breuß, Michael A1 - Hartmann, Carsten T1 - Long Short-Term Memory Neural Network for Temperature Prediction in Laser Powder Bed Additive Manufacturing T2 - Proceedings of SAI Intelligent Systems Conference N2 - n context of laser powder bed fusion (L-PBF), it is known that the properties of the final fabricated product highly depend on the temperature distribution and its gradient over the manufacturing plate. In this paper, we propose a novel means to predict the temperature gradient distributions during the printing process by making use of neural networks. This is realized by employing heat maps produced by an optimized printing protocol simulation and used for training a specifically tailored recurrent neural network in terms of a long short-term memory architecture. The aim of this is to avoid extreme and inhomogeneous temperature distribution that may occur across the plate in the course of the printing process. In order to train the neural network, we adopt a well-engineered simulation and unsupervised learning framework. To maintain a minimized average thermal gradient across the plate, a cost function is introduced as the core criteria, which is inspired and optimized by considering the well-known traveling salesman problem (TSP). As time evolves the unsupervised printing process governed by TSP produces a history of temperature heat maps that maintain minimized average thermal gradient. All in one, we propose an intelligent printing tool that provides control over the substantial printing process components for L-PBF, i.e. optimal nozzle trajectory deployment as well as online temperature prediction for controlling printing quality. KW - Additive manufacturing Laser beam trajectory optimization Powder bed fusion printing Heat simulation Linear-quadratic control Y1 - 2022 SN - 978-3-031-16074-5 U6 - https://doi.org/10.1007/978-3-031-16075-2_8 SN - 978-3-031-16075-2 SP - 119 EP - 132 PB - Springer CY - Cham ER - TY - GEN A1 - Mansouri Yarahmadi, Ashkan A1 - Breuß, Michael A1 - Hartmann, Carsten A1 - Schneidereit, Toni T1 - Unsupervised Optimization of Laser Beam Trajectories for Powder Bed Fusion Printing and Extension to Multiphase Nucleation Models T2 - Mathematical Methods for Objects Reconstruction : From 3D Vision to 3D Printing N2 - In laser powder bed fusion, it is known that the quality of printing results crucially depends on the temperature distribution and its gradient over the manufacturing plate. We propose a computational model for the motion of the laser beam and the simulation of the time-dependent heat evolution over the plate. For the optimization of the laser beam trajectory, we propose a cost function that minimizes the average thermal gradient and allows to steer the laser beam. The optimization is performed in an unsupervised way. Specifically, we propose an optimization heuristic that is inspired by the well-known traveling salesman problem and that employs simulated annealing to determine a nearly optimal pathway. By comparison of the heat transfer simulations of the derived trajectories with trajectory patterns from standard printing protocols we show that the method gives superior results in terms of the given cost functional. KW - Additive manufacturing Multiphase alloys Trajectory optimization Powder bed fusion printing Heat simulation Linear-quadratic control Y1 - 2023 SN - 978-981-99-0775-5 U6 - https://doi.org/10.1007/978-981-99-0776-2_6 SN - 978-981-99-0776-2 SP - 157 EP - 176 PB - Springer CY - Singapor ER - TY - GEN A1 - Masouri Yarahmadi, Ashkan A1 - Breuß, Michael A1 - Hartmann, Carsten T1 - Long Short-Term Memory Neural Network for Temperature Prediction in Laser Powder Bed Additive Manufacturing T2 - arXiv Y1 - 2023 U6 - https://doi.org/10.48550/arXiv.2301.12904 SP - 1 EP - 15 ER - TY - GEN A1 - Delle Site, Luigi A1 - Hartmann, Carsten T1 - Computationally feasible bounds for the free energy of nonequilibrium steady states, applied to simple models of heat conduction T2 - Molecular Physics Y1 - 2024 U6 - https://doi.org/10.1080/00268976.2024.2391484 SN - 0026-8976 PB - Informa UK Limited ER - TY - JOUR A1 - Hartmann, Carsten A1 - Richter, Lorenz T1 - Nonasymptotic Bounds for Suboptimal Importance Sampling JF - SIAM/ASA Journal on Uncertainty Quantification Y1 - 2024 U6 - https://doi.org/10.1137/21M1427760 SN - 2166-2525 VL - 12 IS - 2 SP - 309 EP - 346 PB - Society for Industrial & Applied Mathematics (SIAM) ER - TY - JOUR A1 - Delle Site, Luigi A1 - Hartmann, Carsten T1 - Scaling law for the size dependence of a finite-range quantum gas JF - Physical Review A Y1 - 2024 U6 - https://doi.org/10.1103/PhysRevA.109.022209 SN - 2469-9926 VL - 109 IS - 2 PB - American Physical Society (APS) ER - TY - GEN A1 - Reible, Benedikt A1 - Hille, Julian F. A1 - Hartmann, Carsten A1 - Delle Site, Luigi T1 - Finite size effects and thermodynamic accuracy in many-particle systems T2 - Physical Review Research Y1 - 2023 U6 - https://doi.org/10.1103/PhysRevResearch.5.023156 SN - 2643-1564 VL - 5 IS - 2 SP - 023156-1 EP - 023156-8 ER - TY - GEN A1 - Reible, Benedikt A1 - Hartmann, Carsten A1 - Delle Site, Luigi T1 - Two-sided Bogoliubov inequality to estimate finite-size effects in quantum molecular simulations T2 - Letters in Mathematical Physics Y1 - 2022 U6 - https://doi.org/10.1007/s11005-022-01586-3 SN - 1573-0530 SN - 0377-9017 VL - 112 IS - 5 SP - 1 EP - 17 ER -