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Non-linear model-order reduction based on tensor decomposition and matrix product

IET CONTROL theory AND applications 2018年第16期12卷 2253-2262页

作者： Li, Zhen Jiang, Yaolin Xu, Kangli Xinjiang Univ Coll Math & Syst Sci Urumqi 830046 Peoples R China Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Shaanxi Peoples R China

In this study, based on tensor decomposition and matrix product, the authors investigate two model-order reduction (MOR) methods for the quadratic-bilinear (QB) systems which are equivalently transformed from the non-linear input-output systems. Since the quadratic term coefficient of the QB system can be considered as the matricisation of a tensor, they propose two computationally efficient ways to obtain the reduced system by using tensor calculus. First, the Tucker decomposition of tensors is used to deal with the quadratic term coefficient of the QB system. The transformational matrix is constructed by applying the analysis of matrix product. Then, they get the reduced QB system which can match the first several expansion coefficients of the original output. Besides, they propose another MOR method based on the CANDECOMP/PARAFAC decomposition. These two methods can avoid large computational complexity in the process of computing the reduced system. Moreover, the error estimation and stability of the authors' MOR methods are discussed. The efficiency of their MOR methods is illustrated by two numerical examples and they show their competitiveness when compared to the proper orthogonal decomposition method.

关键词： matrix algebra reduced order systems tensors nonlinear model-order reduction tensor decomposition matrix product quadratic-bilinear systems nonlinear input-output systems quadratic term coefficient tensor calculus transformational matrix reduced QB system expansion coefficients MOR method CANDECOMP PARAFAC decomposition orthogonal decomposition method Tucker decomposition

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numerical Analysis of Gradient Planar Waveguides in Frequency Domain 17

Numerical Analysis of Gradient Planar Waveguides in Frequenc...

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17th IEEE International conference on Mathematical methods in Electromagnetic theory (MMET)

作者： Fitio, V. Yaremchuk, I. Bendzyak, A. Bobitski, Y. Lviv Polytech Natl Univ Dept Photon Lvov Ukraine Univ Rzeszow Fac Math & Nat Sci Rzeszow Poland

ISBN: (纸本)9781538654385

Developed a numerical method for calculating propagation constants of localized modes of planar waveguides, as well as the solution of the stationary Schrodinger equation. The method is based on the Fourier transform of the wave equation. As a result, we obtain an integral equation in which the integral is replaced by summation. Ultimately, we obtain the problem of linear algebra with eigenvalues and eigenvectors. The method is verified on many examples. It is numerically stable and provides high accuracy of calculation

关键词： Wave equation planar waveguide Fourier transform convolution

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Universality laws for randomized dimension reduction, with applications

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INFORMATION AND INFERENCE-A JOURNAL OF THE IMA 2018年第3期7卷 337-446页

作者： Oymak, Samet Tropp, Joel A. Simons Inst Theory Comp Melvin Calvin Lab Berkeley CA 94720 USA CALTECH Comp & Math Sci 1200 E Calif BlvdMC 305-16 Pasadena CA 91125 USA

Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to the data. This dimension reduction procedure succeeds when it preserves certain geometric features of the set. The question is how large the embedding dimension must be to ensure that randomized dimension reduction succeeds with high probability. This article studies a natural family of randomized dimension reduction maps and a large class of data sets. It proves that there is a phase transition in the success probability of the dimension reduction map as the embedding dimension increases. For a given data set, the location of the phase transition is the same for all maps in this family. Furthermore, each map has the same stability properties, as quantified through the minimum RSV. These results can be viewed as new universality laws in high-dimensional stochastic geometry. Universality laws for randomized dimension reduction have many applications in applied mathematics, signal processing and statistics. They yield design principles for numerical linear algebra algorithms, for compressed sensing measurement ensembles and for random linear codes. Furthermore, these results have implications for the performance of statistical estimation methods under a large class of random experimental designs.

关键词： conic geometry convex geometry dimension reduction invariance principle limit theorem random code random matrix randomized numerical linear algebra signal reconstruction statistical estimation stochastic geometry universality

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General linear methods for Time-Dependent PDEs 1

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16th International conference on Hyperbolic Problems - theory, Numerics, and applications

作者： Jaust, Alexander Schutz, Jochen Hasselt Univ Fac Sci Agoralaan Gebouw D B-3590 Diepenbeek Belgium

ISBN: (数字)9783319915487

ISBN: (纸本)9783319915487;9783319915470

The hybridized discontinuous Galerkin method has been successfully applied to time-dependent problems using implicit time integrators. These integrators stem from the 'classical' class of backward differentiation formulae (BDF) and diagonally implicit Runge-Kutta (DIRK) methods. We extend this to the class of general linear methods (GLMs) that unify multistep and multistage methods into one framework. We focus on diagonally implicit multistage integration methods (DIMSIMs) that can have the same desirable stability properties like DIRK methods while also having high stage order. The presented numerical results confirm that the applied DIMSIMs achieve expected approximation properties for linear and nonlinear problems.

关键词： General linear method Hybridized discontinuous galerkin method Time-dependent CFD

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Intellectualization Of Computation Based On Neural Networks For Mathematical Modeling

Intellectualization Of Computation Based On Neural Networks ...

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IEEE International conference on Advanced Trends in Information theory (ATIT)

作者： Alexander Khimich Volodymyr Sydoruk Pavlo Yershov Department of numerical methods and computer modeling VM Glushkov Institute of Cybernetics of NAS of Ukraine Kyiv Ukraine

ISBN: (数字)9781728161440

ISBN: (纸本)9781728161457

The problem of automation of efficient algorithm choice for solving linear algebra problems with a priori undefined structure of sparse matrices is considered. An approach of matrix classification and selection of an effective algorithm based on a visual portrait of a sparse matrix using a neural networks is proposed. Datasets for training of convolutional neural network "Sparse Matrix Vision" were prepared. Computational experiments, conducted in a scope of a current research showed that the algorithm chosen by neural network is effective for a specific problem.

关键词： Sparse matrices Classification algorithms Kernel Biological neural networks Computational modeling Training

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linear two-dimensional models of anisotropic plates in high approximations 7

Linear two-dimensional models of anisotropic plates in high ...

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7th International conference on Computational methods in Structural Dynamics and Earthquake Engineering, COMPDYN 2019

作者： Tovstik, Petr E. Ivanov, Denis S. Naumova, Natalia V. Tovstik, Tatiana P. Zelinskaya, Anna V. St. Petersburg State University Universitetskaya nab. 7-9 St. Petersburg199034 Russia Institute for Problems in Mechanical Engineering RAS Bolshoy pr. V. O. 61 St. Petersburg199178 Russia

ISBN: (纸本)9786188284470

Thin elastic anisotropic plates heterogeneous in the thickness direction are studied. Delivering of 2D approximate models of plates and shells is one of the classical problems of mechanics. In the present study, 2D models are delivered by using asymptotic expansions of solutions of 3D equations of the theory of elasticity in power series of a small thickness parameter. The zero asymptotic approximation gives equations that coincide with the Kirchhof–Love model if we use in-plane elasticity relations. If the elastic moduli are of identical order, then this model gives results acceptable for applications. In the opposite case, it is desirable to construct higher approximations. For particular types of anisotropy, 2D models of the second-order of accuracy were constructed earlier, and here we present a second-order model for a plate made of a heterogeneous material with general anisotropy described by 21 elastic moduli. The structure of the model and the differential orders of PDE is the same as for the Timoshenko–Reissner model, but equations are significantly more cumbersome. For a plate infinite in the tangential directions, there exists a simple harmonic solution. This solution allows us to estimate an error of 2D models compared with the exact solution of 3D equations of the theory of elasticity. The model is used to solve static and vibration problems. Some numerical examples are considered. © 2019 The authors.

关键词： Elastic moduli

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Fuzzy c-Regression Models with Cluster Characteristics Clarification

Fuzzy c-Regression Models with Cluster Characteristics Clari...

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International conference on Fuzzy theory and it's applications (iFUZZY)

作者： Shinpei Nasada Katsuhiro Honda Seiki Ubukata Akira Notsu Graduate School of Engineering Osaka Prefecture University Sakai Osaka Japan Graduate School of Humanities and Sustainable System Sciences Osaka Prefecture University Sakai Osaka Japan

ISBN: (数字)9781728108407

ISBN: (纸本)9781728108414

In order to improve the comparative interpretability among cluster-wise local regression models, this paper proposes a modified fuzzy c-regression models (FCRM), which is a fuzzy c-means (FCM)-type switching regression. Based on the combined concepts of ridge regression and intra-cluster exclusive variable selection, cluster-wise meaningful explanatory variables are emphasized. Additionally, it is further extended with the LASSO concept for reducing the inappropriate influences of larger coefficient values. The characteristics of the proposed methods are demonstrated through some numerical experiments.

关键词： Switches Iterative methods linear programming Clustering algorithms Input variables Predictive models numerical models

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-gain control on positive impulsive system via a hybrid proportional plus integral algorithm

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IET Control theory & applications 2019年第7期13卷 898-904页

作者： Hao Chen Tao Zhan Qinzhen Huang College of Electrical and Information Engineering Southwest Minzu University Chengdu 610041 People's Republic of China Department of Applied Mathematics University of Waterloo Waterloo Ontario N2L 3G1 Canada School of Mathematics Shandong University Jinan Shandong 250100 People's Republic of China

In this study, the -gain control issues on positive system are investigated. A hybrid proportional impulsive with integral (PII) control scheme is proposed. This impulse-time-dependent control algorithm uses the proportional control action at impulse instants for stabilising, and applies the integral control strategy between impulse time intervals for improving the state convergence, respectively. The average impulsive interval approach and co-positive Lyapunov function method are employed to derive the sufficient conditions. Then -gain performance of the impulsive positive system can be guaranteed by solving the linear programming problem. In addition, iterative convex optimisation algorithm is presented for the design of PII control gain matrices. numerical examples illustrate the expected results of this design.

关键词： Lyapunov methods matrix algebra gain control control system synthesis linear programming time-varying systems iterative methods convex programming stability impulse time intervals co-positive Lyapunov function method impulsive positive system iterative convex optimisation algorithm PII control gain matrices positive impulsive system hybrid proportional plus integral algorithm integral control scheme impulse-time-dependent control algorithm impulse instants impulsive interval approach integral control strategy 𝒦1 stability proportional control action Kp ℒ1 -gain control issues linear programming problem

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Mean-square error constrained approach to robust stochastic iterative learning control

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IET CONTROL theory AND applications 2018年第1期12卷 38-44页

作者： Li, Li Liu, Yang Yang, Zhile Yang, Xiaofeng Li, Kang Harbin Inst Technol Ultraprecis Optoelect Instrumentat Engn Ctr Harbin Heilongjiang Peoples R China Harbin Inst Technol Dept Control Sci & Engn Harbin Heilongjiang Peoples R China Chinese Acad Sci Shenzhen Inst Adv Technol Shenzhen Peoples R China Fudan Univ Dept Microelect Shanghai Peoples R China Queens Univ Belfast Sch Elect Elect Engn & Comp Sci Belfast Antrim North Ireland

A Kalman filtering-based robust iterative learning control algorithm is proposed in this study for linear stochastic systems with uncertain dynamics and unknown noise statistics. Firstly, a learning gain matrix is designed for the nominal case by minimising the trace of the mean-square matrix of the input tracking error. Theoretical results show that the proposed algorithm guarantees not only the asymptotic but also monotonic convergence of the input tracking error in the mean-square error sense, especially when random noises are Gaussian distributed the proposed algorithm is further proved to be asymptotically efficient. In addition, a new mean-square error constrained approach is presented in designing the robust learning gain matrix, taking into account model uncertainties. A sufficient condition is provided such that the mean-square matrix of the input tracking error is constrained within a predesigned upper bound which can monotonically converge to zero. Finally, numerical examples considering both structured and unstructured model uncertainties are included to illustrate the effectiveness of the proposed algorithms.

关键词： Kalman filters robust control iterative learning control Gaussian distribution mean square error methods matrix algebra mean-square error constrained approach Kalman filtering-based robust iterative learning control algorithm linear stochastic systems mean-square matrix random noises Gaussian distribution robust learning gain matrix

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Serial and parallel approaches for image segmentation by numerical minimization of a second-order functional

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APPLIED MATHEMATICS AND COMPUTATION 2018年 318卷 153-175页

作者： Zanella, R. Porta, F. Ruggiero, V. Zanetti, M. Univ Ferrara Math & Comp Sci Dept Ferrara Italy Univ Trento Informat & Commun Technol Dept Trento Italy

Because of its attractive features, second order segmentation has shown to be a promising tool in remote sensing. A known drawback about its implementation is computational complexity, above all for large set of data. Recently in Zanetti et al. [1], an efficient version of the block-coordinate descent algorithm (BCDA) has been proposed for the minimization of a second order elliptic approximation of the Blake-Zissermann functional. Although the parallelization of linear algebra operations is expected to increase the performance of BCDA when addressing the segmentation of large-size gridded data (e.g., full-scene images or Digital Surface Models (DSMs)), numerical evidence shows that this is not sufficient to get significant reduction of computational time. Therefore a novel approach is proposed which exploits a decomposition technique of the image domain into tiles. The solution can be computed by applying BCDA on each tile in parallel way and combining the partial results corresponding to the different blocks of variables through a proper interconnection rule. We prove that this parallel method (OPARBCDA) generates a sequence of iterates which converges to a critical point of the functional on the level set devised by the starting point. Furthermore, we show that the parallel method can be efficiently implemented even in a commodity multicore CPU. numerical results are provided to evaluate the efficiency of the parallel scheme on large images in terms of computational cost and its effectiveness with respect to the behavior on the tile junctions. (C) 2017 Elsevier Inc. All rights reserved.

关键词： Segmentation Blake-Zisserman functional Domain decomposition Block coordinate descent methods Parallel interconnection rule

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