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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

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

arXiv

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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

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Parametric S-Parameter Prediction Using Deep Learning

Parametric S-Parameter Prediction Using Deep Learning

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IEEE Topical Meeting on Electrical Performance of Electronic Packaging (EPEPS)

作者： Vinayak Bansal Lihong Feng Valentin de la Rubia Peter Benner Department of Chemical Engineering Indian Institute of Technology Delhi India Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Germany Departamento de Mateádtica Aplicada a las TIC Universidad Politécnica de Madrid Madrid Spain

We construct a neural network model of S-parameters, from which the S-parameters can be quickly pre-dicted. Numerical tests on a filter model show that the proposed method accurately predicts the S-parameters with mul... 详细信息

ISBN: (数字)9798350351231

ISBN: (纸本)9798350351248

关键词： Deep learning Accuracy Transfer functions Predictive models Stability analysis Scattering parameters Numerical models Feedforward neural networks Numerical stability Electronics packaging

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Non-intrusive Time-POD for Optimal control of a Fixed-Bed Reactor for CO 2 Methanation

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IFAC-PapersOnLine 2021年第3期54卷 122-127页

作者： Jens Bremer Jan Heiland Peter Benner Kai Sundmacher Max Planck Institute Magdeburg Dpt. Process Systems Engineering Sandtorstraße 2 39106 Magdeburg Germany and Otto von Guericke University Magdeburg Chair for Process Systems Engineering Universitätsplatz 2 39106 Magdeburg (Sundmacher) Max Planck Institute Magdeburg Dpt. Computational Methods in Systems and Control Theory and Otto von Guericke University Magdeburg Fakultät für Mathematik

The optimization of a controlled process in a simulation without access to the model itself is a common scenario and very relevant to many chemical engineering applications. A general approach is to apply a black-box optimization algorithm to a parameterized control scheme. The success then depends on the quality of the parametrization that should be low-dimensional though rich enough to express the salient features. This work proposes using solution snapshots to extract dominant modes of the temporal dynamics of a process and use them for low-dimensional parametrizations of control functions. The approach is called proper orthogonal decomposition in time (time-POD). We provide theoretical reasoning and illustrate the performance for the optimal control of a methanation reactor.

关键词： Optimal control Model order reduction Proper orthogonal decomposition Fixed-bed reactor Carbon dioxide methanation Nonlinear programming Black-box model

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Efficient structure-preserving support tensor train machine

arXiv

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arXiv 2020年

作者： Kour, Kirandeep Benner, Peter Dolgov, Sergey Stoll, Martin Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems MagdeburgD-39106 Germany Department of Mathematical Sciences University of Bath BathBA2 7AY United Kingdom Faculty of Mathematics Technische Universität Chemnitz ChemnitzD-09107 Germany

An increasing amount of collected data are high-dimensional multi-way arrays (tensors), and it is crucial for efficient learning algorithms to exploit this tensorial structure as much as possible. The ever present curse of dimensionality for high dimensional data and the loss of structure when vectorizing the data motivates the use of tailored low-rank tensor classification methods. In the presence of small amounts of training data, kernel methods offer an attractive choice as they provide the possibility for a nonlinear decision boundary. We develop the Tensor Train Multi-way Multi-level Kernel (TT-MMK), which combines the simplicity of the Canonical Polyadic decomposition, the classification power of the Dual Structure-preserving Support Vector Machine, and the reliability of the Tensor Train (TT) approximation. We show by experiments that the TT-MMK method is usually more reliable computationally, less sensitive to tuning parameters, and gives higher prediction accuracy in the SVM classification when benchmarked against other state-of-the-art techniques. Copyright © 2020, The Authors. All rights reserved.

关键词： Tensors

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ON THE EXISTENCE AND UNIQUENESS OF THE SOLUTION OF A PARABOLIC OPTIMAL control PROBLEM WITH UNCERTAIN INPUTS

arXiv

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arXiv 2018年

作者： Benner, Peter Onwunta, Akwum Stoll, Martin Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstrasse 1 Magdeburg39106 Germany Department of Computer Science University of Maryland College ParkMD20742 United States Technische Universität Chemnitz Faculty of Mathematics Professorship Scientific Computing Chemnitz09107 Germany

In this note, we consider the existence and uniqueness of the solution of a time-dependent optimal control problem constrained by a partial differential equation with uncertain inputs. Relying on the Lions’ Lemma for deterministic problems, we furthermore characterize the optimal control of the stochastic problem. Copyright © 2018, The Authors. All rights reserved.

关键词： Optimal control systems

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Topical Issue Scientific Machine Learning (1/2)

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GAMM Mitteilungen 2021年第1期44卷 e202100010-e202100010页

作者： Benner, Peter Klawonn, Axel Stoll, Martin Computational Methods in Systems and Control Theory Max Planck institute for Dynamics of Complex Technical Systems Magdeburg Germany Fakultät für Mathematik Otto-von-Guericke Universität Magdeburg Germany Department of Mathematics and Computer Science University of Cologne Germany Center for Data and Simulation Science University of Cologne Germany Chair of Scientific Computing Department of Mathematics TU Chemnitz Germany

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Adjoint-Based Optimal Boundary control of a Stefan Problem System Fully Coupled with Navier-Stokes Equations

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PAMM 2016年第1期16卷

作者： Björn Baran Jan Heiland Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 39106 Magdeburg

Free boundary and moving boundary problems, that can be used to model crystal growth or the solidification and melting of pure materials, receive growing attention in science and technology. The optimal control of these problems appear even more interesting since certain desired shapes of the boundaries improve, e.g., the material quality in the case of crystal growth. We consider the so called two-phase Stefan problem that models a solid and a liquid phase separated by a moving interface. In the work presented, we take a sharp interface model approach and define a quadratic tracking-type cost functional that penalizes the deviation of the interface from the desired state at a final time as well as the control costs. Following the “optimize-then-discretize” paradigm, we formulate a first order optimality system using the formal Lagrange approach and derive the adjoint PDE system that provides the needed gradient of the cost functional. By means of an example setup of a container with an in- and outflow of water and a cooling unit at the bottom, we illustrate how the derived formulations can be used to achieve a desired interface between the solid and the fluid phase by controlling the flow at the inlet. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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A Cache-Aware Implementation of the Spectral Divide-and-Conquer Approach for the Non-Symmetric Generalized Eigenvalue Problem

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PAMM 2014年第1期14卷

作者： Peter Benner Martin Köhler Jens Saak Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 39106 Magdeburg

We propose a new implementation of the sign function based spectral divide-and-conquer method for the generalized non-symmetric eigenvalue problem. The basic idea is to use the generalized matrix sign function to split the spectrum and the corresponding deflating subspaces and to build a recursive scheme on top of this. The method focuses on an extensive usage of scalable level 3 BLAS operations in order to achieve a good performance on modern computer architectures which makes it computationally superior to current implementations of the classical QZ algorithm. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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A Reformulated Low-Rank ADI Iteration with Explicit Residual Factors

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PAMM 2013年第1期13卷

作者： Peter Benner Patrick Kürschner Jens Saak Max Planck Institute for Dynamics of Complex Technical Systems: Computational Methods in Systems and Control Theory Sandtorstr. 1 39106 Magdeburg

Based on our recent findings [1, 2] regarding the low-rank ADI iteration for large-scale Lyapunov equations, we propose a mathematically equivalent formulation of the LR-ADI whose iteration is directly connected to low rank factors of the Lyapunov residual. If complex shift parameters occur and are handled efficiently [1], this reformulation is slightly more efficient from a computational point of view, since it guarantees that the right hand sides of all linear systems that need to be solved are real. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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