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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

GR decompositions and their relations to Cholesky-like factorizations

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arXiv 2020年

作者： Benner, Peter Penke, Carolin Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 Magdeburg39106 Germany

For a given matrix, we are interested in computing GR decompositions A = GR, where G is an isometry with respect to given scalar products. The orthogonal QR decomposition is the representative for the Euclidian scalar product. For a signature matrix, a respective factorization is given as the hyperbolic QR decomposition. Considering a skew-symmetric matrix leads to the symplectic QR decomposition. The standard approach for computing GR decompositions is based on the successive elimination of subdiagonal matrix entries. For the hyperbolic and symplectic case, this approach does in general not lead to a satisfying numerical accuracy. An alternative approach computes the QR decomposition via a Cholesky factorization, but also has bad stability. It is improved by repeating the procedure a second time. In the same way, the hyperbolic and the symplectic QR decomposition are related to the LDLT and a skew-symmetric Cholesky-like factorization. We show that methods exploiting this connection can provide better numerical stability than elimination-based *** Codes 65F99 Copyright © 2020, The Authors. All rights reserved.

关键词： Factorization

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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Inf-Sup-Constant-Free State Error Estimator for Model Order Reduction of Parametric systems in Electromagnetics

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arXiv 2021年

作者： Chellappa, Sridhar Feng, Lihong de la Rubia, Valentín Benner, Peter Department of Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg39106 Germany Departamento de Matemática Aplicada a las TIC ETSI de Telecomunicación Universidad Politécnica de Madrid Madrid28040 Spain

A reliable model order reduction process for parametric analysis in electromagnetics is detailed. Special emphasis is placed on certifying the accuracy of the reduced-order model. For this purpose, a sharp state error estimator is proposed. Standard a posteriori state error estimation for model order reduction relies on the inf-sup constant. For parametric systems, the inf-sup constant is parameter-dependent. The a posteriori error estimation for systems with very small or vanishing inf-sup constant poses a challenge, since it is inversely proportional to the inf-sup constant, resulting in overly pessimistic error estimation especially at and around resonance frequencies. Such systems appear in electromagnetics since the inf-sup constant values are close to zero at points close to resonant frequencies, where they eventually vanish. We propose a novel a posteriori state error estimator which avoids the calculation of the inf-sup constant. The proposed state error estimator is compared with the standard error estimator and a recently proposed one in the literature. It is shown that our proposed error estimator outperforms both existing estimators. Numerical experiments are performed on real-life microwave devices such as narrowband and wideband antennas, two types of dielectric resonator filters as well as a dual-mode waveguide filter. These examples show the capabilities and efficiency of the proposed methodology. © 2021, CC BY.

关键词： Galerkin methods

Fast a posteriori state error estimation for reliable frequency sweeping in microwave circuits via the reduced-basis method

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arXiv 2021年

作者： de la Rubia, Valentín Chellappa, Sridhar Feng, Lihong Benner, Peter Departamento de Matemática Aplicada a las TIC ETSI de Telecomunicación Universidad Politécnica de Madrid Madrid28040 Spain Department of Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg39106 Germany

We develop a compact, reliable model order reduction approach for fast frequency sweeps in microwave circuits by means of the reduced-basis method. Contrary to what has been previously done, special emphasis is placed on certifying the accuracy of the reduced-order model with respect to the original full-order model in an effective and efficient way. Previous works on model order reduction accuracy certification rely on costly a posteriori error estimators, which typically require expensive inf-sup constant evaluations of the underlying full-order model. This scenario is often too time-consuming and unaffordable in electromagnetic applications. As a result, less expensive and heuristic error estimators are commonly used instead. Very often, one is interested in knowing about the full state vector, instead of just some output quantities derived from the full state. Therefore, error estimators for the full state vector become relevant. In this work, we detail the frequency behavior of both the electric field and the state error when an approximation to the electric field solution is carried out. Both field quantities share the same frequency behavior. Based on this observation, we focus on the efficient estimation of the electric field state error and propose a fast evaluation of the reduced-order model state error in the frequency band of analysis, minimizing the number of full-order model evaluations. This methodology is of paramount importance to carry out a reliable fast frequency sweep in microwave circuits. Finally, real-life applications will illustrate the capabilities and efficiency of the proposed approach. © 2021, CC BY.

关键词： Computer aided design

Orlando tools: Energy research application development through convergence of grid and cloud computing 4th

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Orlando tools: Energy research application development throu...

4th Russian Supercomputing Days Conference, RuSCDays 2018

作者： Feoktistov, Alexander Gorsky, Sergei Sidorov, Ivan Kostromin, Roman Edelev, Alexei Massel, Lyudmila Matrosov Institute for System Dynamics and Control Theory of SB RAS Irkutsk Russia Melentiev Energy Systems Institute of SB RAS Irkutsk Russia

ISBN: (纸本)9783030058067

The paper addresses the relevant problem related to the development of scientific applications (applied software packages) to solve large-scale problems in heterogeneous distributed computing environments that can include various infrastructures (clusters, Grid systems, clouds) and provide their integrated use. We propose a new approach to the development of applications for such environments. It is based on the integration of conceptual and modular programming. The application development is implemented with a special framework named Orlando Tools. In comparison to the known tools, used for the development and execution of distributed applications in the current practice, Orlando Tools provides executing application jobs in the integrated environment of virtual machines that include both the dedicated and non-dedicated resources. The distributed computing efficiency is improved through the multi-agent management. Experiments of solving the large-scale practical problems of energy security research show the effectiveness of the developed application for solving the aforementioned problem in the environment that supports the hybrid computational model including Grid and cloud computing. © 2019, Springer Nature Switzerland AG.

关键词： Energy security

Model order reduction for gas and energy networks

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arXiv 2020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 counter the volatile nature of renewable energy sources, gas networks take a vital role. But, to ensure fulfillment of contracts under these circumstances, a vast number of possible scenarios, incorporating uncertain supply and demand, has to be simulated ahead of time. This many-query gas network simulation task can be accelerated by model reduction, yet, large-scale, nonlinear, parametric, hyperbolic partial differential(-algebraic) equation systems, modeling natural gas transport, are a challenging application for model order reduction algorithms. For this industrial application, we bring together the scientific computing topics of: mathematical modeling of gas transport networks, numerical simulation of hyperbolic partial differential equation, and parametric model reduction for nonlinear systems. This research resulted in the morgen (Model Order Reduction for Gas and Energy Networks) software platform, which enables modular testing of various combinations of models, solvers, and model reduction methods. In this work we present the theoretical background on systemic modeling and structured, data-driven, system-theoretic model reduction for gas networks, as well as the implementation of morgen and associated numerical experiments testing model reduction adapted to gas network *** Codes 93-04, 76N15, 93B20 Copyright © 2020, The Authors. All rights reserved.

关键词： Nonlinear equations

Constrained Gaussian Process Learning for Model Predictive control ⁎

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IFAC-PapersOnLine 2020年第2期53卷 971-976页

作者： Janine Matschek Andreas Himmel Kai Sundmacher Rolf Findeisen Laboratory for Systems Theory and Automatic Control Otto von Guericke University Magdeburg Germany Process Systems engineering Otto von Guericke University Magdeburg Germany Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Germany

Many control tasks can be formulated as tracking problems of a known or unknown reference signal. examples are motion compensation in collaborative robotics, the synchronisation of oscillations for power systems or the reference tracking of recipes in chemical process operation. Both the tracking performance and the stability of the closed-loop system depend strongly on two factors: Firstly, they depend on whether the future reference signal required for tracking is known, and secondly, whether the system can track the reference at all. This paper shows how to use machine learning, i.e. Gaussian processes, to learn a reference from (noisy) data while guaranteeing trackability of the modified desired reference predictions within the framework of model predictive control. Guarantees are provided by adjusting the hyperparameters via a constrained optimisation. Two specific scenarios, i.e. asymptotically constant and periodic REFERENCES, are discussed.

关键词： Gaussian processes trajectory tracking learning supported model predictive control

Adjacency-based, non-intrusive reduced-order modeling for fluid-structure interactions

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PAMM 2023年第4期23卷

作者： Leonidas Gkimisis Thomas Richter Peter Benner Computational Methods in Systems and Control Theory (CSC) Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Germany Faculty of Mathematics Institute for Analysis and Numerics Otto-von-Guericke Otto-von-Guericke-Universität Magdeburg Universitätsplatz 2 Magdeburg Germany

Non-intrusive model reduction is a promising solution to system dynamics prediction, especially in cases where data are collected from experimental campaigns or proprietary software simulations. In this work, we present a method for non-intrusive model reduction applied to Fluid-Structure Interaction (FSI) problems. The approach is based on the a priori known sparsity of the full-order system operators, which is dictated by grid adjacency information. In order to enforce this type of sparsity, we solve a “local”, regularized least-squares problem for each degree of freedom on a grid, considering only the training data from adjacent degrees of freedom (DoFs), thus making computation and storage of the inferred full-order operators feasible. After constructing the non-intrusive, sparse full-order model (FOM), Proper Orthogonal Decomposition (POD) is used for its projection to a reduced dimension subspace and thus the construction of a reduced-order model (ROM). The methodology is applied to the challenging Hron-Turek benchmark FSI3, for Re = 200. A physics-informed, non-intrusive ROM is constructed to predict the two-way coupled dynamics of a solid with a deformable, slender tail, subject to an incompressible, laminar flow. Results considering the accuracy and predictive capabilities of the inferred reduced models are discussed.

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