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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

Model order reduction via substructuring for a nonlinear, differential-algebraic machine tool model with moving loads

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Model order reduction via substructuring for a nonlinear, di...

92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)

作者： Aumann, Quirin Benner, Peter Saak, Jens Vettermann, Julia Mathematics in Industry and Technology Faculty of Mathematics Technische Universitat Chemnitz Reichenhainer Str. 41 Chemnitz09126 Germany Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 Magdeburg39106 Germany

Machine tools are permanently exposed to complex static, dynamic and thermic loads. This often results in an undesired dis¬placement of the tool center point (TCP), causing errors in the production process and thus limiting the achievable workpiece quality. Recent research efforts try to counter these effects by process-parallel solutions utilizing machine internal data. Therefore, fast simulation models are a fundamental requirement. Here, model order reduction (MOR) becomes crucial. The resulting low-dimensional models are required for various applications, e.g., in digital twins, the correction of thermally in¬duced errors at the TCP during the production process as well as for lifetime calculations in predictive maintenance. In this contribution, we present a strategy of MOR for a coupled thermo-mechanical model with a nonlinear subsystem and moving loads, using the example of a feed axis with nonlinear machine components. Applying tailored substructuring tech¬niques, we are able to separate the linear and nonlinear system components. This allows to apply classic linear MOR methods to the much larger linear part, whereas the small nonlinear part is kept, and thus enables drastically reduced computing times. The relative movement is considered by a switched system approach. Transient thermo-mechanical interactions of the feed axis are calculated in a final investigation, comparing the performance of the resulting reduced-order model and the original one. © 2023 The Authors.

关键词： Machine tools

Fast and reliable reduced-order models for cardiac electrophysiology

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GAMM Mitteilungen 2023年第3-4期46卷 e202370014-e202370014页

作者： Chellappa, Sridhar Cansız, Barış Feng, Lihong Benner, Peter Kaliske, Michael Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Germany Institute for Structural Analysis Technische Universität Dresden Dresden Germany

Mathematical models of the human heart increasingly play a vital role in understanding the working mechanisms of the heart, both under healthy functioning and during disease. The ultimate aim is to aid medical practitioners diagnose and treat the many ailments affecting the heart. Towards this, modeling cardiac electrophysiology is crucial as the heart's electrical activity underlies the contraction mechanism and the resulting pumping action. Apart from modeling attempts, the pursuit of efficient, reliable, and fast solution algorithms has been of great importance in this context. The governing equations and the constitutive laws describing the electrical activity in the heart are coupled, nonlinear, and involve a fast moving wave front, which is generally solved by the finite element method. The numerical treatment of this complex system as part of a virtual heart model is challenging due to the necessity of fine spatial and temporal resolution of the domain. Therefore, efficient surrogate models are needed to predict the electrical activity in the heart under varying parameters and inputs much faster than the finely resolved models. In this work, we develop an adaptive, projection-based reduced-order surrogate model for cardiac electrophysiology. We introduce an a posteriori error estimator that can accurately and efficiently quantify the accuracy of the surrogate model. Using the error estimator, we systematically update our surrogate model through a greedy search of the parameter space. Furthermore, using the error estimator, the parameter search space is dynamically updated such that the most relevant samples get chosen at every iteration. The proposed adaptive surrogate model is tested on three benchmark models to illustrate its efficiency, accuracy, and ability of generalization. © 2024 The Authors. GAMM - Mitteilungen published by Wiley-VCH GmbH.

关键词： Heart

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

Adaptively restarted block Krylov subspace methods with low-synchronization skeletons

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arXiv 2022年

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

With the recent realization of exascale performace by Oak Ridge National Laboratory’s Frontier supercomputer, reducing communication in kernels like QR factorization has become even more imperative. Low-synchronization Gram-Schmidt methods, first introduced in [K. Swirydowicz, ´ J. Langou, S. Ananthan, U. Yang, and S. Thomas, Low Synchronization Gram-Schmidt and Generalized Minimum Residual Algorithms, Numer. Lin. Alg. Appl., Vol. 28(2), e2343, 2020)], have been shown to improve the scalability of the Arnoldi method in high-performance distributed computing. Block versions of low-synchronization Gram-Schmidt show further potential for speeding up algorithms, as column-batching allows for maximizing cache usage with matrix-matrix operations. In this work, low-synchronization block Gram-Schmidt variants from [E. Carson, K. Lund, M. Rozložník, and S. Thomas, Block Gram-Schmidt algorithms and their stability properties, Lin. Alg. Appl., 638, pp. 150–195, 2022] are transformed into block Arnoldi variants for use in block full orthogonalization methods (BFOM) and block generalized minimal residual methods (BGMRES). An adaptive restarting heuristic is developed to handle instabilities that arise with the increasing condition number of the Krylov basis. The performance, accuracy, and stability of these methods are assessed via a flexible benchmarking tool written in MATLAB. The modularity of the tool additionally permits generalized block inner products, like the global inner *** Codes 65F10, 65F25, 65F50, 15-04 Copyright © 2022, The Authors. All rights reserved.

关键词： Stability

A physics-encoded Fourier neural operator approach for surrogate modeling of divergence-free stress fields in solids

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arXiv 2024年

作者： Khorrami, Mohammad S. Goyal, Pawan Mianroodi, Jaber R. Svendsen, Bob Benner, Peter Raabe, Dierk Microstructure Physics and Alloy Design Max-Planck Institute for Sustainable Materials 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 the current work is the development of a so-called physics-encoded Fourier neural operator (PeFNO) for surrogate modeling of the quasi-static equilibrium stress field in solids. Rather than accounting for constraints from physics in the loss function as done in the (now standard) physics-informed approach, the physics-encoded approach incorporates or"encodes" such constraints directly into the network or operator architecture. As a result, in contrast to the physics-informed approach in which only training is physically constrained, both training and output are physically constrained in the physics-encoded approach. For the current constraint of divergence-free stress, a novel encoding approach based on a stress potential is proposed. As a"proof-of-concept" example application of the proposed PeFNO, a heterogeneous polycrystalline material consisting of isotropic elastic grains subject to uniaxial extension is considered. Stress field data for training are obtained from the numerical solution of a corresponding boundary-value problem for quasi-static mechanical equilibrium. This data is also employed to train an analogous physics-guided FNO (PgFNO) and physics-informed FNO (PiFNO) for comparison. As confirmed by this comparison and as expected on the basis of their differences, the output of the trained PeFNO is significantly more accurate in satisfying mechanical equilibrium than the output of either the trained PgFNO or the trained PiFNO. Copyright © 2024, The Authors. All rights reserved.

关键词： Polycrystalline materials

The Fréchet derivative of the tensor t-function

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arXiv 2023年

作者： Lund, Kathryn Schweitzer, Marcel Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 Magdeburg39106 Germany School of Mathematics and Natural Sciences Bergische Universität Wuppertal Wuppertal42097 Germany

The tensor t-function, a formalism that generalizes the well-known concept of matrix functions to third-order tensors, is introduced in [K. Lund, The tensor t-function: a definition for functions of third-order tensors, Numer. Linear Algebra Appl. 27 (3), e2288]. In this work, we investigate properties of the Fréchet derivative of the tensor t-function and derive algorithms for its efficient numerical computation. Applications in condition number estimation and nuclear norm minimization are explored. Numerical experiments implemented by the t-Frechet toolbox hosted at https://***/katlund/t-frechet illustrate properties of the t-function Fréchet derivative, as well as the efficiency and accuracy of the proposed *** Codes 15A69, 65F60, 65F35 Copyright © 2023, The Authors. All rights reserved.

关键词： Tensors

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

Low-rank-modified Galerkin methods for the Lyapunov equation

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arXiv 2023年

作者： Lund, Kathryn Palitta, Davide Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 Magdeburg39106 Germany Dipartimento di Matematica Piazza di Porta S. Donato 5 Bologna40126 Italy

Of all the possible projection methods for solving large-scale Lyapunov matrix equations, Galerkin approaches remain much more popular than minimal-residual ones. This is mainly due to the different nature of the projected problems stemming from these two families of methods. While a Galerkin approach leads to the solution of a low-dimensional matrix equation per iteration, a matrix least-squares problem needs to be solved per iteration in a minimal-residual setting. The significant computational cost of these least-squares problems has steered researchers towards Galerkin methods in spite of the appealing properties of minimal-residual schemes. In this paper we introduce a framework that allows for modifying the Galerkin approach by low-rank, additive corrections to the projected matrix equation problem with the two-fold goal of attaining monotonic convergence rates similar to those of minimal-residual schemes while maintaining essentially the same computational cost of the original Galerkin method. We analyze the well-posedness of our framework and determine possible scenarios where we expect the residual norm attained by two low-rank-modified variants to behave similarly to the one computed by a minimal-residual technique. A panel of diverse numerical examples shows the behavior and potential of our new *** Codes 65F45, 65F50, 65F10, 65N22, 65J10 Copyright © 2023, The Authors. All rights reserved.

关键词： Galerkin methods