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Next-Gen gas network simulation

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arXiv 2021年

作者： Himpe, Christian Grundel, Sara Benner, Peter Computational Methods in Systems and Control Theory Group The Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstraße 1 MagdeburgD-39106 Germany

To overcome many-query optimization, control, or uncertainty quantification work loads in reliable gas and energy network operations, model order reduction is the mathematical technology of choice. To this end, we enhance the model, solver and reductor components of the morgen platform, introduced in HIMPE ET AL [J. Math. Ind. 11:13, 2021], and conclude with a mathematically, numerically and computationally favorable model-solver-reductor ensemble. Copyright © 2021, The Authors. All rights reserved.

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An artificial neural network for surrogate modeling of stress fields in viscoplastic polycrystalline materials

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arXiv 2022年

作者： Khorrami, Mohammad S. Mianroodi, Jaber Rezaei Siboni, Nima H. Goyal, Pawan Svendsen, Bob Benner, Peter Raabe, Dierk Microstructure Physics and Alloy Design Max-Planck-Institut für Eisenforschung Düsseldorf Germany Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Germany Material Mechanics RWTH Aachen University Aachen Germany

The purpose of this work is the development of an artificial neural network (ANN) for surrogate modeling of the mechanical response of viscoplastic grain microstructures. To this end, a U-Net-based convolutional neural network (CNN) is trained to account for the history dependence of the material behavior. The training data take the form of numerical simulation results for the von Mises stress field under quasi-static tensile loading. The trained CNN (tCNN) can accurately reproduce both the average response as well as the local von Mises stress field. The tCNN calculates the von Mises stress field of grain microstructures not included in the training dataset about 500 times faster than its calculation based on the numerical solution with a spectral solver of the corresponding initial-boundary-value problem. The tCNN is also successfully applied to other types of microstructure morphologies (e.g., matrix-inclusion type topologies) and loading levels not contained in the training dataset. Copyright © 2022, The Authors. All rights reserved.

关键词： Deep learning

Machine learning for material characterization with an application for predicting mechanical properties

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GAMM Mitteilungen 2021年第1期44卷 e202100003-e202100003页

作者： Stoll, Anke Benner, Peter Data-Mining and Machine Learning Fraunhofer Institute for Machine Tools and Forming Technology IWU Chemnitz Germany Computational Methods in Systems and Control Theory The Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Germany

Currently, the growth of material data from experiments and simulations is expanding beyond processable amounts. This makes the development of new data-driven methods for the discovery of patterns among multiple lengthscales and time-scales and structure-property relationships essential. These data-driven approaches show enormous promise within materials science. The following review covers machine learning (ML) applications for metallic material characterization. Many parameters associated with the processing and the structure of materials affect the properties and the performance of manufactured components. Thus, this study is an attempt to investigate the usefulness of ML methods for material property prediction. Material characteristics such as strength, toughness, hardness, brittleness, or ductility are relevant to categorize a material or component according to their quality. In industry, material tests like tensile tests, compression tests, or creep tests are often time consuming and expensive to perform. Therefore, the application of ML approaches is considered helpful for an easier generation of material property information. This study also gives an application of ML methods on small punch test (SPT) data for the determination of the property ultimate tensile strength for various materials. A strong correlation between SPT data and tensile test data was found which ultimately allows to replace more costly tests by simple and fast tests in combination with ML. © 2021 The Authors. GAMM - Mitteilungen published by Wiley-VCH GmbH.

关键词： Machine learning

Reorthogonalized Pythagorean variants of block classical Gram-Schmidt

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arXiv 2024年

作者： Carson, Erin Lund, Kathryn Ma, Yuxin Oktay, Eda Department of Numerical Mathematics Faculty of Mathematics and Physics Charles University Sokolovská 49/83 Praha 8186 75 Czech Republic Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 Magdeburg39106 Germany Computational Mathematics Theme Building R71 STFC Rutherford Appleton Laboratory Harwell Oxford Didcot OxfordshireOX11 0QX United Kingdom Department of Mathematics Chemnitz University of Technology Reichenhainer Str. 41 Chemnitz09126 Germany

Block classical Gram-Schmidt (BCGS) is commonly used for orthogonalizing a set of vectors X in distributed computing environments due to its favorable communication properties relative to other orthogonalization approaches, such as modified Gram-Schmidt or Householder. However, it is known that BCGS (as well as recently developed low-synchronization variants of BCGS) can suffer from a significant loss of orthogonality in finite-precision arithmetic, which can contribute to instability and inaccurate solutions in downstream applications such as s-step Krylov subspace methods. A common solution to improve the orthogonality among the vectors is reorthogonalization. Focusing on the "Pythagorean" variant of BCGS, introduced in [E. Carson, K. Lund, & M. Rozložník. SIAM J. Matrix Anal. Appl. 42(3), pp. 1365–1380, 2021], which guarantees an O(Ε)κ2(X) bound on the loss of orthogonality as long as O(Ε)κ2(X) MSC Codes 65-04, 65F25, 65G50, 65Y20 Copyright © 2024, The Authors. All rights reserved.

关键词： Matrix algebra

On the loss of orthogonality in low-synchronization variants of reorthogonalized block classical Gram-Schmidt

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arXiv 2024年

作者： Carson, Erin Lund, Kathryn Ma, Yuxin Oktay, Eda Department of Numerical Mathematics Faculty of Mathematics and Physics Charles University Sokolovská 49/83 Praha 8186 75 Czech Republic Computational Mathematics Theme Building R71 STFC Rutherford Appleton Laboratory Harwell Oxford Didcot OxfordshireOX11 0QX United Kingdom Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 Magdeburg39106 Germany Department of Mathematics Chemnitz University of Technology Reichenhainer Str. 41 Chemnitz09126 Germany

Interest in communication-avoiding orthogonalization schemes for high-performance computing has been growing recently. This manuscript addresses open questions about the numerical stability of various block classical Gram-Schmidt variants that have been proposed in the past few years. An abstract framework is employed, the flexibility of which allows for new rigorous bounds on the loss of orthogonality in these variants. We first analyze a generalization of (reorthogonalized) block classical Gram-Schmidt and show that a "strong" intrablock orthogonalization routine is only needed for the very first block in order to maintain orthogonality on the level of the unit roundoff. Then, using this variant, which has four synchronization points per block column, we remove the synchronization points one at a time and analyze how each alteration affects the stability of the resulting method. Our analysis shows that the variant requiring only one synchronization per block column cannot be guaranteed to be stable in practice, as stability begins to degrade with the first reduction of synchronization points. Our analysis of block methods also provides new theoretical results for the single-column case. In particular, it is proven that DCGS2 from [Bielich, D. et al. Par. Comput. 112 (2022)] and CGS-2 from [Świrydowicz, K. et al, Num. Lin. Alg. Appl. 28 (2021)] are as stable as Householder QR. Numerical examples from the BlockStab toolbox are included throughout, to help compare variants and illustrate the effects of different choices of intraorthogonalization *** Codes 65-04, 65F25, 65G50, 65Y20 Copyright © 2024, The Authors. All rights reserved.

关键词： Subroutines

Constructing the Optimal Strategy for a Drone in an Obstacle Avoidance Problem

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Constructing the Optimal Strategy for a Drone in an Obstacle...

International Conference on control systems, Mathematical Modelling, Automation and Energy Efficiency (SUMMA)

作者： Oleg Malafeyev Irina Zaitseva Mark Akbashev Tatiana Smirnova Sergei Miheev Evgeny Kolpak Department of Modelling in Social and Economical Systems Saint Petersburg State University St. Petersburg Russia Department of Higher Mathematics and Physics Russian State Hydrometeorological University St. Petersburg Russia Department of Modeling of Socio-economic systems Saint Petersburg State University St Petersburg Russia Department of mathematical theory of control systems modeling Saint-Petersburg State University St. Petersburg Russia Department of computational methods of mechanics of deformable body Saint-Petersburg State University St. Petersburg Russia

ISBN: (数字)9798331532178

ISBN: (纸本)9798331532185

This article discusses the problem of building an optimal strategy for a drone in the task of chasing a target and avoiding obstacles. The paper analyzes a mathematical model of a game with incomplete information, in which players make decisions based on limited information about each other's condition. Theorems related to the existence of successful strategies for players in this task are presented. The study presents strategies for a drone in conditions of limited information and identifies optimal approaches to solving the problem of harassment. A strategy has been formulated for the drone in conditions of limited information and determine the optimal approaches to solving the task of pursuit. The results demonstrate in the MATLAB/SCRIPT application program the existence of an optimal strategy for unmanned aerial vehicles, which ensures effective overcoming of obstacles under various conditions and constraints. The results obtained can be applied to develop algorithms for controlling unmanned systems in pursuit scenarios.

关键词： Autonomous systems Buildings Games control systems Autonomous aerial vehicles Mathematical models Energy efficiency MATLAB Collision avoidance Drones

PD controllers to solve single-input, index-1 DAE based LQR problems

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PD controllers to solve single-input, index-1 DAE based LQR ...

European control Conference (ECC)

作者： Chayan Bhawal Jan Heiland Peter Benner Department of Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg

ISBN: (数字)9783907144022

ISBN: (纸本)9781728188133

In this paper, we present a method to compute the optimal trajectories of a linear quadratic regulator (LQR) problem corresponding to a single input, index-1 constant coefficient DAE system. Further, we also show that using a suitably designed proportional-derivative (PD) state-feedback controller one can force the trajectories of the corresponding DAE system to its optimal trajectories. Unlike the results present in the literature, the results in this paper are applicable for any arbitrary initial condition of the system.

关键词： Trajectory Indexes Matrix converters PD control Optimal control Regulators controllability

Frequency scaling and energy efficiency regarding the Gauss-Jordan elimination scheme with application to the matrix-sign-function on OpenPOWER 8

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Frequency scaling and energy efficiency regarding the Gauss-...

作者： Köhler, Martin Saak, Jens Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems MagdeburgD-39104 Germany

The Gauss-Jordan Elimination scheme is an alternative to the LU decomposition for solving linear systems or computing the inverse of a matrix. We develop a multi-GPU aware implementation of this algorithm on an OpenPOWER 8 system with application to the Matrix Sign Function. Thereby, we analyze the influence of the CPU clock frequency scaling on the overall energy consumption. The results show possible energy saving of 14.2% without a noteworthy increase of the runtime. © 2018 John Wiley & Sons, Ltd.

关键词： Energy efficiency

Comparing (Empirical-Gramian-Based) Model Order Reduction Algorithms

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arXiv 2020年

作者： Himpe, Christian Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 Magdeburg39106 Germany

In this work, the empirical-Gramian-based model reduction methods: Empirical poor man’s truncated balanced realization, empirical approximate balancing, empirical dominant subspaces, empirical balanced truncation, and empirical balanced gains are compared in a non-parametric and two parametric variants, via ten error measures: Approximate Lebesgue L0, L1, L2, L∞, Hardy H2, H∞, Hankel, Hilbert-Schmidt-Hankel, modified induced primal, and modified induced dual norms, for variants of the thermal block model reduction benchmark. This comparison is conducted via a new meta-measure for model reducibility called MORscore. inMSC Codes 93A15, 93B11, 65Y20 Copyright © 2020, The Authors. All rights reserved.

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