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Synchronization in Multiplex systems with Simplex Interactions Beyond All-to-All Coupling

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Synchronization in Multiplex Systems with Simplex Interactio...

Neurotechnologies and Neurointerfaces (CNN), International Conference

作者： Tetyana Laptyeva Mikhail Ivanchenko Department of Control Theory and Dynamics of Systems Lobachevsky University Nizhny Novgorod Russia Department of Applied Mathematics Lobachevsky University Nizhny Novgorod Russia

ISBN: (数字)9798350390926

ISBN: (纸本)9798350390933

关键词： Couplings Multiplexing Complex networks Nonhomogeneous media Synchronization Oscillators Neurotechnology Hysteresis Biological neural networks

Active learning enhanced deep-learning surrogate model for fast MEMS design with high-dimensional design parameter spaces

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Active learning enhanced deep-learning surrogate model for f...

IEEE International Conference on Nano/Micro Engineered and Molecular systems (NEMS)

作者： Chenzi Wang Lihong Feng Wenshuai Lu Wei Bian Zheng You Peter Benner Department of Precision Instrument Tsinghua University Beijing China Department of Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Germany

ISBN: (数字)9798350359831

ISBN: (纸本)9798350359848

MEMS devices suffer from errors in manufacturing processes such as lithography, etching, thinning, etc. These errors cause non-negligible deviations between the actual device performance and the ideal performance obtained from finite element method (FEM) simulation in the design stage. Often, parametric sweeps via FEM simulations at heuristically selected geometrical and material parameter samples are implemented, in order to analyze the corresponding device performance deviations. This analysis is empirical and often fails due to large number of possible design parameter variations caused by manufacturing. Performing parametric sweeps for all possible parameter instances would result in an exponential increase in FEM simulations. In this paper, we propose a novel active learning enhanced deep-learning surrogate model, which replaces the FEM simulation and faithfully predicts the device performance deviations under numerous parameter variances. This provides a powerful tool for predicting device yield at the design stage. Furthermore, the proposed active learning technique could be applied to efficient training of deep learning models for other MEMS design problems.

关键词： Micromechanical devices Performance evaluation Training Nanoelectromechanical systems Training data Predictive models Data models

Efficient structure-preserving support tensor train machine

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The Journal of Machine Learning Research

The Journal of Machine Learning Research 2023年第1期24卷 98-119页

作者： Kirandeep Kour Peter Benner Sergey Dolgov Martin Stoll Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Germany Department of Mathematical Sciences University of Bath Bath UK Faculty of Mathematics Technische Universität Chemnitz Chemnitz Germany

An increasing amount of the 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.

关键词： tensor decomposition support vector machine kernel approximation high-dimensional data classification

Parametric S-Parameter Prediction Using Deep Learning

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Parametric S-Parameter Prediction Using Deep Learning

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

Explosive synchronization in multiplex neuron-glial networks

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arXiv 2023年

作者： Laptyeva, Tetyana Jalan, Sarika Ivanchenko, Mikhail Department of Control Theory and Systems Dynamics Lobachevsky State University of Nizhny Novgorod Nizhny Novgorod Russia Complex Systems Lab Department of Physics Indian Institute of Technology Indore Indore Simrol452020 India Department of Applied Mathematics Laboratory of Systems Medicine of Healthy Aging Lobachevsky State University of Nizhny Novgorod Nizhny Novgorod Russia

Explosive synchronization refers to an abrupt (first order) transition to non-zero phase order parameter in oscillatory networks, underpinned by the bistability of synchronous and asynchronous states. Growing evidence suggests that this phenomenon might be no less general then the celebrated Kuramoto scenario that belongs to the second order universality class. Importantly, the recent examples demonstrate that explosive synchronization can occur for certain network topologies and coupling types, like the global higher-order coupling, without specific requirements on the individial oscillator dynamics or dynamics-network correlations. Here we demonstrate a rich picture of explosive synchronization and desynchronization transitions in multiplex networks, where it is sufficient to have a single random sparsly connected layer with higher-order coupling terms (and not necessarily in the synchronization regime on its own), the other layer being a regular lattice without own phase transitions at all. Moreover, explosive synchronization emerges even when the random layer has only low-order pairwise coupling, althoug the hysteresis interval becomes narrow and explosive desynchronization is no longer observed. The relevance to the normal and pathological dynamics of neural-glial networks is pointed out. © 2023, CC BY.

关键词： Synchronization

INTERPOLATORY H2-OPTIMALITY CONDITIONS FOR STRUCTURED LINEAR TIME-INVARIANT systems

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arXiv 2023年

作者： Mlinarić, Petar Benner, Peter Gugercin, Serkan Department of Mathematics Virginia Tech BlacksburgVA24061 United States Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg39106 Germany Department of Mathematics Division of Computational Modeling and Data Analytics Academy of Data Science Virginia Tech BlacksburgVA24061 United States

Interpolatory necessary optimality conditions for H2-optimal reduced-order modeling of unstructured linear time-invariant (LTI) systems are well-known. Based on previous work on L2-optimal reduced-order modeling of stationary parametric problems, in this paper we develop and investigate optimality conditions for H2-optimal reduced-order modeling of structured LTI systems, in particular, for second-order, port-Hamiltonian, and time-delay systems. Under certain diagonalizability assumptions, we show that across all these different structured settings, bitangential Hermite interpolation is the common form for optimality, thus proving a unifying optimality framework for structured reduced-order modeling. Copyright © 2023, The Authors. All rights reserved.

关键词： Linear time-invariant system

DC-DC Converters Optimization in Case of Large Variation in the Load

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arXiv 2024年

作者： Domyshev, Alexander Chistyakova, Elena Dreglea, Aliona Sidorov, Denis Liu, Fang Melentiev Energy Systems Institute Siberian Branch Russian Academy Sciences Irkutsk Russia Harbin Institute of Technology Harbin China Irkutsk National Research Technical University Irkutsk Russia Institute for System Dynamics and Control Theory Siberian Branch Russian Academy Sciences Irkutsk Russia Department of Automation Central South University Changsha China

The method for controlling a DC-DC converter is proposed to ensures the high quality control at large fluctuations in load currents by using differential gain control coefficients and second derivative control. Various implementations of balancing the currents of a multiphase DC-DC converter are discussed, with a focus on achieving accurate current regulation without introducing additional delay in the control system. Stochastic particle swarm optimization method is used to find optimal values of the PID controller parameters. An automatic constraint-handling in optimization are also discussed as relevant techniques in the *** Codes 34H05 34A09 © 2024, CC BY.

关键词： Stochastic systems

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

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