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arXiv 2023年

作者： Maier, Gregor Hamaekers, Jan Martilotti, Dominik-Sergio Ziebarth, Benedikt Fraunhofer Institute for Algorithms and Scientific Computing SCAI Schloss Birlinghoven Sankt Augustin53757 Germany Institut für Numerische Simulation Universität Bonn Friedrich-Hirzebruch-Allee 7 Bonn53115 Germany Fraunhofer Center for Machine Learning Schloss Birlinghoven Sankt Augustin53757 Germany Schott AG Hattenbergstrasse 10 Mainz55122 Germany

Many modern-day applications require the development of new materials with specific properties. In particular, the design of new glass compositions is of great industrial interest. Current machine learning methods for learning the composition-property relationship of glasses promise to save on expensive trial-and-error approaches. Even though quite large datasets on the composition of glasses and their properties already exist (i.e., with more than 350,000 samples), they cover only a very small fraction of the space of all possible glass compositions. This limits the applicability of purely data-driven models for property prediction purposes and necessitates the development of models with high extrapolation power. In this paper, we propose a neural network model which incorporates prior scientific and expert knowledge in its learning pipeline. This informed learning approach leads to an improved extrapolation power compared to blind (uninformed) neural network models. To demonstrate this, we train our models to predict three different material properties, that is, the glass transition temperature, the Young’s modulus (at room temperature), and the shear modulus of binary oxide glasses which do not contain sodium. As representatives for conventional blind neural network approaches we use five different feed-forward neural networks of varying widths and depths. For each property, we set up model ensembles of multiple trained models and show that, on average, our proposed informed model performs better in extrapolating the three properties of previously unseen sodium borate glass samples than all five conventional blind models. © 2023, CC BY-SA.

关键词： Extrapolation

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Erratum to “Multilevel B-Spline Repulsive Energy in Nanomodeling of Graphenes” [Journal of Surface Engineered Materials and Advanced Technology Vol. 4 No. 2 (April 2014) 75-86]

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Journal of Surface Engineered Materials and Advanced Technology 2015年第2期5卷 84-84页

作者： Maharavo Randrianarivony Virtual Material Design Fraunhofer Institute for Algorithms and Scientific Computing SCAI Schloss Birlinghoven Sankt Augustin Germany

Quantum energies which are used in applications are usually composed of repulsive and attractive terms. The objective of this study is to use an accurate and efficient fitting of the repulsive energy instead of using standard parametrizations. The investigation is based on Density Functional Theory and Tight Binding simulations. Our objective is not only to capture the values of the repulsive terms but also to efficiently reproduce the elastic properties and the forces. The elasticity values determine the rigidity of a material when some traction or load is applied on it. The pair-potential is based on an exponential term corrected by B-spline terms. In order to accelerate the computations, one uses a hierarchical optimization for the B-splines on different levels. Carbon graphenes constitute the configurations used in the simulations. We report on some results to show the efficiency of the B-splines on different levels.

关键词： Repulsive potential B-spline Force Elastic stress Hierarchy

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ProML--the protein markup language for specification of protein sequences, structures and families

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In silico biology 2002年第3期2卷 313-24页

作者： Daniel Hanisch Ralf Zimmer Thomas Lengauer Fraunhofer Institute for Algorithms and Scientific Computing (SCAI) Schloss Birlinghoven D-53754 Sankt Augustin Germany.

We propose a specification language ProML for protein sequences, structures, and families based on the open XML standard. The language allows for portable, system-independent, machine-parsable and human-readable representation of essential features of proteins. The language is of immediate use for several bioinformatics applications: we discuss clustering of proteins into families and the representation of the specific shared features of the respective clusters. Moreover, we use ProML for specification of data used in fold recognition bench-marks exploiting experimentally derived distance constraints.

关键词： Protein Markup Language ProML XML protein properties proteinfamilies protein protein structures distance constraints protein clusters

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Semi-Lagrangian lattice Boltzmann method for compressible flows

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Physical Review E 2020年第5期101卷 053306-053306页

作者： Dominik Wilde Andreas Krämer Dirk Reith Holger Foysi Department of Mechanical Engineering University of Siegen Paul-Bonatz-Straße 9-11 D-57076 Siegen-Weidenau Germany Institute of Technology Resource and Energy-efficient Engineering (TREE) Bonn-Rhein-Sieg University of Applied Sciences Grantham-Allee 20 D-53757 Sankt Augustin Germany National Heart Lung and Blood Institute National Institutes of Health Bethesda Maryland 20892 USA Fraunhofer Institute for Algorithms and Scientific Computing (SCAI) Schloss Birlinghoven D-53754 Sankt Augustin Germany

This work thoroughly investigates a semi-Lagrangian lattice Boltzmann (SLLBM) solver for compressible flows. In contrast to other LBM for compressible flows, the vertices are organized in cells, and interpolation polynomials up to fourth order are used to attain the off-vertex distribution function values. Differing from the recently introduced Particles on Demand (PoD) method [Dorschner, Bösch, and Karlin, Phys. Rev. Lett. 121, 130602 (2018)], the method operates in a static, nonmoving reference frame. Yet the SLLBM in the present formulation grants supersonic flows and exhibits a high degree of Galilean invariance. The SLLBM solver allows for an independent time step size due to the integration along characteristics and for the use of unusual velocity sets, like the D2Q25, which is constructed by the roots of the fifth-order Hermite polynomial. The properties of the present model are shown in diverse example simulations of a two-dimensional Taylor-Green vortex, a Sod shock tube, a two-dimensional Riemann problem, and a shock-vortex interaction. It is shown that the cell-based interpolation and the use of Gauss-Lobatto-Chebyshev support points allow for spatially high-order solutions and minimize the mass loss caused by the interpolation. Transformed grids in the shock-vortex interaction show the general applicability to nonuniform grids.

关键词： Kinetic theory Lattice-Boltzmann methods

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Pseudoentropic derivation of the regularized lattice Boltzmann method

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Physical Review E 2019年第2期100卷 023302-023302页

作者： Andreas Krämer Dominik Wilde Knut Küllmer Dirk Reith Holger Foysi Institute of Technology Resource and Energy-efficient Engineering (TREE) Bonn-Rhein-Sieg University of Applied Sciences Grantham-Allee 20 53757 Sankt Augustin Germany National Heart Lung and Blood Institute National Institutes of Health Bethesda Maryland 20892 United States Department of Mechanical Engineering University of Siegen Paul-Bonatz-Straße 9-11 57076 Siegen-Weidenau Germany Fraunhofer Institute for Algorithms and Scientific Computing (SCAI) Schloss Birlinghoven 53754 Sankt Augustin Germany

The lattice Boltzmann method (LBM) facilitates efficient simulations of fluid turbulence based on advection and collision of local particle distribution functions. To ensure stable simulations on underresolved grids, the collision operator must prevent drastic deviations from local equilibrium. This can be achieved by various methods, such as the multirelaxation time, entropic, quasiequilibrium, regularized, and cumulant schemes. Complementing a part of a unified theoretical framework of these schemes, the present work presents a derivation of the regularized lattice Boltzmann method (RLBM), which follows a recently introduced entropic multirelaxation time LBM by Karlin, Bösch, and Chikatamarla (KBC). It is shown that both methods can be derived by locally maximizing a quadratic Taylor expansion of the entropy function. While KBC expands around the local equilibrium distribution, the RLBM is recovered by expanding entropy around a global equilibrium. Numerical tests were performed to elucidate the role of pseudoentropy maximization in these models. Simulations of a two-dimensional shear layer show that the RLBM successfully reproduces the largest eddies even on a 16×16 grid, while the conventional LBM becomes unstable for grid resolutions of 128×128 and lower. The RLBM suppresses spurious vortices more effectively than KBC. In contrast, simulations of the three-dimensional Taylor-Green and Kida vortices show that KBC performs better in resolving small scale vortices, outperforming the RLBM by a factor of 1.8 in terms of the effective Reynolds number.

关键词： Flow instability Shear flows Turbulence

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Erratum to “On DFT Molecular Simulation for Non-Adaptive Kernel Approximation” [Advances in Materials Physics and Chemistry Vol. 4 No. 6 (June 2014) 105-115]

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Advances in Materials Physics and Chemistry 2015年第3期5卷 95-95页

作者： Maharavo Randrianarivony Virtual Material Design Fraunhofer Institute for Algorithms and Scientific Computing SCAI Schloss Birlinghoven Sankt Augustin Germany

The original online version of this article (Randrianarivony, M. (June 2014) On DFT Molecular Simulation for Non-Adaptive Kernel Approximation. Advances in Materials Physics and Chemistry, Vol. 4 No. 6, 105-115. http://***/10.4236/ampc.2014.46013) did not contain any acknowledgment. The author wishes to add the following acknowledgements: Acknowledgements: This work was partially supported by Eurostars Project E!6935 funded by German Federal Ministry of Education and Research.

关键词： DFT Energy Stochastic Covariance Hyperparameter

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Predictive analytics in quality assurance for assembly processes: lessons learned from a case study at an industry 4.0 demonstration cell

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Procedia CIRP 2021年 104卷 641-646页

作者： Peter Burggräf Johannes Wagner Benjamin Heinbach Fabian Steinberg Alejandro R. Pérez M. Lennart Schmallenbach Jochen Garcke Daniela Steffes-lai Moritz Wolter Chair of International Production Engineering and Management (IPEM) Universität Siegen Paul-Bonatz-Straße 9-11 57076 Siegen Germany Fraunhofer Institute for Algorithms and Scientific Computing (SCAI) Schloss Birlinghoven 1 53757 Sankt Augustin Germany Fraunhofer Center for Machine Learning Schloss Birlinghoven 1 53757 Sankt Augustin Germany Institute for Numerical Simulation Universität Bonn Endenicher Allee 19b 53115 Bonn Germany Institute for Computer Science Universität Bonn Endenicher Allee 19a 53115 Bonn Germany

Quality assurance (QA) is an important task in manufacturing to assess whether products meet their specifications. However, QA might be expensive, time-consuming, or incomplete. This paper presents a solution for predictive analytics in QA based on machine sensor values during production while employing specialized machine-learning models for classification in a controlled environment. Furthermore, we present lessons learned while implementing this model, which helps to reduce complexity in further industrial applications. The paper’s outcome proves that the developed model was able to predict product quality, as well as to identify the correlation between machine-status and faulty product occurrence.

关键词： Machine-Learning Predictive Quality Production Quality Assurance Classification

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Efficient solution of ill-posed integral equations through averaging

arXiv

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arXiv 2024年

作者： Griebel, Michael Jahn, Tim Institut für Numerische Simulation Universität Bonn Friedrich-Hirzebruch-Allee 7 Bonn53115 Germany Fraunhofer Institute for Algorithms and Scientific Computing SCAI Schloss Birlinghoven Sankt Augustin53754 Germany Institut für Mathematik TU Berlin Straße des 17. Juni 135 Berlin10623 Germany

This paper discusses the error and cost aspects of ill-posed integral equations when given discrete noisy point evaluations on a fine grid. Standard solution methods usually employ discretization schemes that are directly induced by the measurement points. Thus, they may scale unfavorably with the number of evaluation points, which can result in computational inefficiency. To address this issue, we propose an algorithm that achieves the same level of accuracy while significantly reducing computational costs. Our approach involves an initial averaging procedure to sparsify the underlying grid. To keep the exposition simple, we focus on regularization via the truncated singular value decomposition of one-dimensional ill-posed integral equations that have sufficient smoothness. However, the approach can be generalized to other popular regularization methods and more complicated two- and three-dimensional problems with appropriate *** Codes 65, 65R32, 65R20 © 2024, CC BY.

关键词： Integral equations

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Kernel-based stochastic collocation for the random two-phase navier-stokes equations

arXiv

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arXiv 2018年

作者： Griebel, M. Rieger, C. Zaspel, P. Institute for Numerical Simulation Bonn University Endenicher Allee 19b BonnD-53115 Fraunhofer Institute for Algorithms and Scientific Computing Scai Schloss Birlinghoven Sankt AugustinD-53754 Department of Mathematics Rwth Aachen University Schinkelstr. 2 AachenD-52062 Department of Mathematics and Computer Science University of Basel Spiegelgasse 1 Basel4051

In this work, we apply stochastic collocation methods with radial kernel basis functions for an uncertainty quantification of the random incompressible two-phase Navier-Stokes equations. Our approach is non-intrusive and we use the existing fluid dynamics solver NaSt3DGPF to solve the incompressible two-phase Navier-Stokes equation for each given realization. We are able to empirically show that the resulting kernel-based stochastic collocation is highly competitive in this setting and even outperforms some other standard methods. Copyright © 2018, The Authors. All rights reserved.

关键词： Viscous flow

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High-order semi-Lagrangian kinetic scheme for compressible turbulence

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Physical Review E 2021年第2期104卷 025301-025301页

作者： Dominik Wilde Andreas Krämer Dirk Reith Holger Foysi Department of Mechanical Engineering University of Siegen Paul-Bonatz-Straße 9-11 57076 Siegen-Weidenau Germany Institute of Technology Resource and Energy-efficient Engineering (TREE) Bonn-Rhein-Sieg University of Applied Sciences Grantham-Allee 20 53757 Sankt Augustin Germany Department of Mathematics and Computer Science Freie Universität Berlin Arnimallee 6 14195 Berlin Germany Fraunhofer Institute for Algorithms and Scientific Computing (SCAI) Schloss Birlinghoven 53754 Sankt Augustin Germany

Turbulent compressible flows are traditionally simulated using explicit time integrators applied to discretized versions of the Navier-Stokes equations. However, the associated Courant-Friedrichs-Lewy condition severely restricts the maximum time-step size. Exploiting the Lagrangian nature of the Boltzmann equation's material derivative, we now introduce a feasible three-dimensional semi-Lagrangian lattice Boltzmann method (SLLBM), which circumvents this restriction. While many lattice Boltzmann methods for compressible flows were restricted to two dimensions due to the enormous number of discrete velocities in three dimensions, the SLLBM uses only 45 discrete velocities. Based on compressible Taylor-Green vortex simulations we show that the new method accurately captures shocks or shocklets as well as turbulence in 3D without utilizing additional filtering or stabilizing techniques other than the filtering introduced by the interpolation, even when the time-step sizes are up to two orders of magnitude larger compared to simulations in the literature. Our new method therefore enables researchers to study compressible turbulent flows by a fully explicit scheme, whose range of admissible time-step sizes is dictated by physics rather than spatial discretization.

关键词： Compressible flows Kinetic theory Turbulence Lattice-Boltzmann methods Navier-Stokes equation

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