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Generalized Sparse Grid Interpolation Based on the Fast Discrete Fourier Transform 1

5th Workshop on Sparse Grids and Applications, SGA 2018

作者： Griebel, Michael Hamaekers, Jan Institute for Numerical Simulation University of Bonn Bonn Germany Fraunhofer Institute for Algorithms and Scientific Computing SCAI Schloss Birlinghoven Sankt Augustin Germany

ISBN: (数字)9783030813628

ISBN: (纸本)9783030813611

In (Griebel and Hamaekers, Fast discrete Fourier transform on generalized sparse grids, Sparse grids and Applications, volume 97 of Lecture Notes in Computational Science and Engineering, pages 75–108, Springer, 2014), an algorithm for trigonometric interpolation involving only so-called standard information of multivariate functions on generalized sparse grids has been suggested and a study on its application for the interpolation of functions in periodic Sobolev spaces of dominating mixed smoothness has been presented. In this complementary paper, we now give a slight modification of the proofs, which yields an extension from the pairing (Hs,Hmixt) to the more general pairing (Hs,Hmixt,r) and which in addition results in an improved estimate for the interpolation error. The improved (constructive) upper bound is in particular consistent with the lower bound for sampling on regular sparse grids with r = 0 and s = 0 given in (Dũng, Acta Mathematica Vietnamica, 43(1):83–110, 2018;Dũng et al., Hyperbolic Cross Approximation, Advanced Courses in Mathematics - CRM Barcelona, Birkhäuser/Springer, 2018). © 2021, Springer Nature Switzerland AG.

关键词： Discrete Fourier transforms

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On Multilevel Energy-Based Fragmentation Methods

arXiv

引用

arXiv 2024年

作者： Barker, James Griebel, Michael Hamaekers, Jan Institute for Numerical Simulation University of Bonn Friedrich-Hirzebruch-Allee 7 Bonn53115 Germany Fraunhofer Institute for Algorithms and Scientific Computing SCAI Schloss Birlinghoven 1 Sankt Augustin53757 Germany

Energy-based fragmentation methods approximate the potential energy of a molecular system as a sum of contribution terms built from the energies of particular subsystems. Some such methods reduce to truncations of the many-body expansion (MBE);others combine subsystem energies in a manner inspired by the principle of inclusion/exclusion (PIE). The combinatorial technique of Möbius inversion of sums over partially ordered sets, which generalizes the PIE, is known to provide a non-recursive expression for the MBE contribution terms, and has also been connected to related cluster expansion methods. We build from these ideas a very general framework for decomposing potential functions into energetic contribution terms associated with elements of particular partially ordered sets (posets) and direct products thereof. Specific choices immediately reproduce not only the MBE, but also a number of other existing decomposition forms, including, e.g., the multilevel ML-BOSSANOVA schema. Furthermore, a different choice of poset product leads to a setup familiar from the combination technique for high-dimensional approximation, which has a known connection to quantum-chemical composite methods. We present the ML-SUPANOVA decomposition form, which allows the further refinement of the terms of an MBE-like expansion of the Born-Oppenheimer potential according to systematic hierarchies of ab initio methods and of basis sets. We outline an adaptive algorithm for the a posteori construction of quasi-optimal truncations of this decomposition. Some initial experiments are reported and *** Codes 35J10, 65D40, 65Z05, 92E10, 06A07 © 2024, CC BY.

关键词： Adaptive algorithms

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On Advanced Modeling of Compressors and Weighted Mix Iteration for Simulation of Gas Transport Networks 1

引用

11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, SIMULTECH 2021

作者： Baldin, Anton Cassirer, Kläre Clees, Tanja Klaassen, Bernhard Nikitin, Igor Nikitina, Lialia Pott, Sabine Fraunhofer Institute for Algorithms and Scientific Computing Schloss Birlinghoven Sankt Augustin53754 Germany Bonn-Rhine-Sieg University of Applied Sciences Grantham-Allee 20 Sankt Augustin53754 Germany

ISBN: (数字)9783031231490

ISBN: (纸本)9783031231483

In this paper, the modeling of gas compressors with detailed representation of their calibrated characteristics is considered. A method is developed for transforming the characteristics from the space of calibration data to the space of transport variables in which the network problem is actually solved. This transformation satisfies the general stability conditions necessary for the convergence of Newtonian iterations in solving large scale network problems. In addition, a stabilization method of weighted relaxation for mixing iterations is presented, used to find the detailed gas composition. The tests on a large number of realistic gas networks demonstrate nearly 100% convergence of the methods. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Linear systems

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PERTURBATIONS OF EMBEDDED EIGENVALUES OF ASYMPTOTICALLY PERIODIC MAGNETIC SCHRÖDINGER OPERATORS ON A CYLINDER

arXiv

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arXiv 2025年

作者： Jansen, Jonas Sasane, Sara Maad Treschow, Wilhelm Fraunhofer Institute for Algorithms and Scientific Computing SCAI Schloss Birlinghoven Sankt Augustin53757 Germany Centre for Mathematical Sciences Lund University P.O. Box 118 Lund221 00 Sweden

We investigate the persistence of embedded eigenvalues for a class of magnetic Laplacians on an infinite cylindrical domain. The magnetic potential is assumed to be C2 and asymptotically periodic along the unbounded direction, with an algebraic decay rate towards a periodic background potential. Under the condition that the embedded eigenvalue of the unperturbed operator lies away from the thresholds of the continuous spectrum, we show that the set of nearby potentials for which the embedded eigenvalue persists forms a smooth manifold of finite and even codimension. The proof employs tools from Floquet theory, exponential dichotomies, and Lyapunov–Schmidt reduction. Additionally, we give an example of a potential which satisfies the assumptions of our main *** Codes 35P05, 47A55, 81Q15, 35B20, 35J10, 35J15, 81Q10 Copyright © 2025, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

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Privacy Risk Assessment for Synthetic Longitudinal Health Data

Privacy Risk Assessment for Synthetic Longitudinal Health Da...

引用

69th Annual Meeting of the German Association of Medical Informatics, Biometry and Epidemiology, GMDS 2024

作者： Schneider, Julian Walter, Marvin Otte, Karen Meurers, Thierry Perrar, Ines Nöthlings, Ute Adams, Tim Fröhlich, Holger Prasser, Fabian Fluck, Juliane Kühnel, Lisa Knowledge Management ZB MED - Information Centre for Life Sciences Cologne Germany Medical Informatics Group Berlin Institute of Health at Charité - Universitätsmedizin Berlin Berlin Germany Institute of Nutritional and Food Sciences - Nutritional Epidemiology University of Bonn Bonn Germany Department of Bioinformatics Fraunhofer Institute for Algorithms and Scientific Computing SCAI Sankt Augustin Germany The Agricultural Faculty University of Bonn Bonn Germany Faculty of Technology Bielefeld University Bielefeld Germany

ISBN: (纸本)9781643685366

Introduction A modern approach to ensuring privacy when sharing datasets is the use of synthetic data generation methods, which often claim to outperform classic anonymization techniques in the trade-off between data utility and privacy. Recently, it was demonstrated that various deep learning-based approaches are able to generate useful synthesized datasets, often based on domain-specific analyses. However, evaluating the privacy implications of releasing synthetic data remains a challenging problem, especially when the goal is to conform with data protection guidelines. Methods Therefore, the recent privacy risk quantification framework Anonymeter has been built for evaluating multiple possible vulnerabilities, which are specifically based on privacy risks that are considered by the European Data Protection Board, i.e. singling out, linkability, and attribute inference. This framework was applied to a synthetic data generation study from the epidemiological domain, where the synthesization replicates time and age trends previously found in data collected during the DONALD cohort study (1312 participants, 16 time points). The conducted privacy analyses are presented, which place a focus on the vulnerability of outliers. Results The resulting privacy scores are discussed, which vary greatly between the different types of attacks. Conclusion Challenges encountered during their implementation and during the interpretation of their results are highlighted, and it is concluded that privacy risk assessment for synthetic data remains an open problem. © 2024 The Authors.

关键词： Differential privacy

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New dark matter scenarios with low energy photons and neutrinos

arXiv

引用

arXiv 2023年

作者： Nikitin, Igor Fraunhofer Institute for Algorithms and Scientific Computing Schloss Birlinghoven Sankt Augustin53757 Germany

In this paper, a cosmological model is considered, in which dark matter is emitted by T-symmetric quasi-black holes distributed over galaxies. Low energy photons and neutrinos are taken as candidates for dark matter particles. Photon case can be closed due to the suppression of electromagnetic waves by interstellar/intergalactic medium. For neutrinos, two scenarios are considered. In the first, light neutrinos pair to bosonic quasiparticles that form massive halos around galaxies. In the second, heavier sterile neutrinos form massive halos without pairing. At the observables level, both scenarios turn out to be equivalent to the standard LambdaCDM model. At the same time, the considered model possesses additional sources – quasi-black holes – that can produce the required number of neutrinos in addition to the Big Bang. This opens up additional possibilities for cosmological constructions. The matching of the model with early cosmology and ongoing neutrino experiments is discussed. In addition, the possibility of solving general cosmological problems, including horizon, flatness and cosmological constant problems, as well as Hubble tension, within the framework of the considered model, is discussed. © 2023, CC BY.

关键词： Photons

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Integrating Cloud computing, Bayesian Optimization, and Neural-Additive Modeling for Enhanced CAM Systems in 5-Axis Milling 34

Integrating Cloud Computing, Bayesian Optimization, and Neur...

引用

34th CIRP Design Conference, CIRP 2024

作者： Rudel, Viktor Vinogradov, Georg Ganser, Philipp Bergs, Thomas Vahl, Christopher Frings, Markus König, Valentina Schambach, Maximilian Dietzel, Stefan Königs, Michael Fraunhofer Institute for Production Technology IPT Steinbachstraße 17 Aachen52074 Germany RWTH Aachen University Campus-Boulevard 30 Aachen52074 Germany Fraunhofer Institute for Algorithms and Scientific Computing SCAI Schloss Birlinghoven 1 Sankt Augustin53757 Germany ModuleWorks GmbH Henricistraße 50 Aachen52072 Germany Merantix Momentum Merantix AI Campus Max-Urich-Straße 3 Berlin13355 Germany EXAPT Systemtechnik GmbH Theaterstraße 12 Aachen52062 Germany

This publication introduces the development and application of an advanced CAD/CAM/CAE system that leverages the computational capabilities of an edge-cloud infrastructure. The developed system consists of containerized technology models for various complex process planning simulation tasks in 5-axis-milling, such as toolpath calculation, cutter-workpiece-engagement, uncut chip geometry or cutting force simulations. Moreover, a Bayesian optimization (BO) algorithm is coupled with the system enabling multi-objective optimizations of the considered machining operations by varying predefined CAM-parameters. The result of the optimization consists of a set of Pareto-efficient solutions. Each solution realizes a different tradeoff between the technological objectives of the process planner. Since mastering the complexity of the design space is a major challenge in today's CAM programming workflow, a Neural-Additive Model (NAM) is coupled with the system improving guided search through the configuration/result space. This reduces the convergence time to an optimal CAM parameter set. The coupling of the cloud computing, multi-objective optimization and artificial intelligence method with a CAM-kernel is demonstrated based on the process design of 5-axis milling operations for a blade-integrated disk (blisk). © 2024 The Authors. Published by Elsevier B.V.

关键词： Milling (machining)

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On dark stars, galactic rotation curves and fast radio bursts 9

On dark stars, galactic rotation curves and fast radio burst...

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9th International Conference on Mathematical Modeling in Physical Sciences, IC-MSQUARE 2020

作者： Nikitin, Igor Fraunhofer Institute for Algorithms and Scientific Computing Schloss Birlinghoven Sankt Augustin53757 Germany

This paper is a continuation of our recent work on Radial Dark Matter stars (RDM-stars), black holes, coupled with radial flows of dark matter. As a galaxy model, it produces flat rotation curves, approximately valid for many galaxies far from the center. In this paper, more detailed modeling is carried out, including the vicinity of the galactic center. Assuming that the distribution of stellar black holes repeats the distribution of luminous matter, we get a perfect match between the model rotation curves and the observed ones. Further, using numerical integration, we examine the gravitational field of an individual RDM-star. The computation shows the event horizon being erased and rapidly increasing mass density arising instead (mass inflation). In this regime, we apply the previously constructed Planck star model, where at high densities a repulsive force occurs (quantum bounce). In our stationary model, the evolution of a Planck star has stopped under the pressure of dark matter flows. This system is considered as a possible source of Fast Radio Bursts (FRBs). In a scenario involving an asteroid falling onto an RDM-star, the model reproduces the correct frequency range of FRBs. Their total energy, coherence and short duration are explained as well. © Published under licence by IOP Publishing Ltd.

关键词： Stars

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Mathematical modeling and visualization of topologically non-trivial solutions in general relativity 9

Mathematical modeling and visualization of topologically non...

引用

9th International Conference on Mathematical Modeling in Physical Sciences, IC-MSQUARE 2020

作者： Nikitin, Igor Fraunhofer Institute for Algorithms and Scientific Computing Schloss Birlinghoven Sankt Augustin53757 Germany

In general relativity, there is a class of solutions that currently do not have observed analogues, but on which the theory is shaped, giving an understanding what is fundamentally possible within its framework. Such solutions include wormholes, tunnels that connect distant regions in spacetime. Although not a single wormhole has yet been discovered, there is a large number of works devoted to their study, thanks to which wormholes as a class of solutions become firmly established in modern science. In this paper, we consider two topologically nontrivial types of solutions related to wormholes. First: wormholes that can open and close. In this relation, we will discuss topological censorship theorems, which under certain conditions prohibit changing topology. We will also discuss known ways to circumvent these theorems. Using analytical and numerical methods, as well as visualization, we will construct an example of an opening and closing wormhole with the dimensions of the central black hole in the Milky Way galaxy. Our construction continues the work by Kardashev, Novikov and Shatskiy, in which a static wormhole with the same parameters was considered. The second type is a modification of Visser's dihedral wormhole solution for a dynamic case. © Published under licence by IOP Publishing Ltd.

关键词： Visualization

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Galactic model with a phase transition from dark matter to dark energy 24

Galactic model with a phase transition from dark matter to d...

引用

24th Workshop What Comes Beyond the Standard Models

作者： Nikitin, I. Fraunhofer Institute for Algorithms and Scientific Computing Schloss Birlinghoven Sankt Augustin53757 Germany

This work continues the construction of a recently proposed model of dark matter stars. In this model, dark matter quanta are sterile massless particles that are emitted from the central regions of the galaxy in the radial direction. As a result, at large distances r from the center of the galaxy, the mass density of dark matter has the form ρ ∼ r-2, in contrast to the homogeneous model ρ = Const. In the cosmological context, the homogeneous model with massless particles corresponds to the radiation epoch of the expansion of the universe, while the proposed inhomogeneous model turns out to be equivalent to ΛCDM. In this paper, scenarios will be considered in which the radial emission of dark matter is brought into hydrostatic equilibrium with a uniform background. It is shown that solutions exist if the uniform background has an equation of state typical for dark energy. Thus, this model describes a phase transition from dark matter inside the galaxy to dark energy outside of it. The specific mechanism for such a transition could be Bose-Einstein condensation. In addition, the question of what happens if dark matter particles are not sterile, for example, are photons of the Standard Model, is considered. © 2021 DMFA zaloznistvo. All rights reserved.

关键词： Galaxies

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