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Efficient a Posteriori Error Control of a Consistent Atomistic/Continuum Coupling Method for Two Dimensional Crystalline Defects

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arXiv 2022年

作者： Wang, Yangshuai Wang, Hao Department of Mathematics University of British Columbia 1984 Mathematics Road Vancouver Canada School of Mathematics Sichuan University No. 24 Yihuan Road Chengdu China

adaptive atomistic/continuum (a/c) coupling method is an important method for the simulation of material and atomistic systems with defects to achieve the balance of accuracy and efficiency. Residual based a posteriori error estimator is often employed in the adaptive algorithm to provide an estimate of the error of the strain committed by applying the continuum approximation for the atomistic system and the finite element discretization in the continuum region. In this work, we propose a theory based approximation for the residual based a posteriori error estimator which greatly improves the efficiency of the adaptivity. In particular, the numerically expensive modeling residual is only computed exactly in a small region around the coupling interface but replaced by a theoretically justified approximation by the coarsening residual outside that region. We present a range of adaptive computations based on our modified a posteriori error estimator and its variants for different types of crystalline defects some of which are not considered in previous related literature of the adaptive a/c methods. The numerical results show that, compared with the original residual based error estimator, the adaptive algorithm using the modified error estimator with properly chosen parameters leads to the same optimal convergence rate of the error but reduces the computational cost by one order with respect to the number of degrees of freedom. © 2022, CC0.

关键词： adaptive algorithms

Low-Complexity Implementation of a Data-Reuse RLS Algorithm

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Low-Complexity Implementation of a Data-Reuse RLS Algorithm

International Conference on Telecommunications and Signal Processing (TSP)

作者： Ionut-Dorinel Fî ciu Cristian-Lucian Stanciu Camelia Elisei-Iliescu Cristian Anghel Radu-Mihnea Udrea Department of Telecommunications University Politehnica of Bucharest Bucharest Romania

ISBN: (数字)9781665469487

ISBN: (纸本)9781665469494

The recursive least-squares (RLS) family of adaptive algorithms is an attractive solution for adaptive systems due to their capacity of mitigating the correlation of input signals. The associated forgetting factor parameter is used to compromise between convergence speed/tracking and accuracy. This paper proposes a data-reuse methodology for a low-complexity RLS adaptive algorithm based on the dichotomous coordinate descent iterations, which offers improved tracking performances and an acceptable overall arithmetic workload, suitable for hardware implementations.

关键词： adaptive systems Simulation Signal processing algorithms adaptive algorithms Signal processing Complexity theory Telecommunications

A POSTERIORI ERROR ESTIMATE AND ADAPTIVITY FOR QM/MM MODELS OF CRYSTALLINE DEFECTS

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arXiv 2022年

作者： Wang, Yangshuai Kermode, James R. Ortner, Christoph Zhang, Lei University of British Columbia 1984 Mathematics Road VancouverBC Canada Warwick Centre for Predictive Modelling School of Engineering University of Warwick CoventryCV4 7AL United Kingdom School of Mathematical Sciences Institute of Natural Sciences and MOE-LSC Shanghai Jiao Tong University Shanghai200240 China

Hybrid quantum/molecular mechanics (QM/MM) models play a pivotal role in molecular simulations. These models provide a balance between accuracy, surpassing pure MM models, and computational efficiency, offering advantages over pure QM models. adaptive approaches have been developed to further improve this balance by allowing on-the-fly selection of the QM and MM subsystems as necessary. We propose a novel and robust adaptive QM/MM method for practical material defect simulations. To ensure mathematical consistency with the QM reference model, we employ machine-learning interatomic potentials (MLIPs) as the MM models [13, 31]. Our adaptive QM/MM method utilizes a residual-based error estimator that provides both upper and lower bounds for the approximation error, thus indicating its reliability and efficiency. Furthermore, we introduce a novel adaptive algorithm capable of anisotropically updating the QM/MM partitions. This update is based on the proposed residual-based error estimator and involves solving a free interface motion problem, which is efficiently achieved using the fast marching method. We demonstrate the robustness of our approach via numerical tests on a wide range of crystalline defects. © 2022, CC0.

关键词： adaptive algorithms

Time and Energy Efficient Contention Resolution in Asynchronous Shared Channels

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arXiv 2022年

作者： De Marco, Gianluca Kowalski, Dariusz R. Stachowiak, Grzegorz Dipartimento di Informatica University of Salerno Italy School of Computer and Cyber Sciences Augusta University GA United States

A shared channel (also called a multiple access channel), introduced nearly 50 years ago, is among the most popular and widely studied models of communication and distributed computing. In a nutshell, a number of stations, independently activated over time, is able to communicate by transmitting and listening to a shared channel in discrete time slots, and a message is successfully delivered to all stations if and only if its source station is the only transmitter at a time. Despite a vast amount of work in the last decades, many fundamental questions remain open in the realistic situation where stations do not start synchronously but are awaken in arbitrary times (called dynamic or asynchronous scenario). What is the impact of an asynchronous start on channel utilization? How important is the knowledge/estimate of the number of contenders? Could non-adaptive protocols be asymptotically as efficient as adaptive ones? In this work we present a broad picture of results answering the abovementioned questions for the fundamental problem of Contention resolution, in which each of the contending stations needs to broadcast successfully its message. We show that adaptive algorithms or algorithms with the knowledge of the contention size k achieve a linear O(k) message latency even if the channel feedback is restricted to simple acknowledgements in case of successful transmissions and in the absence of synchronization. This asymptotically optimal performance cannot be extended to other settings: we prove that there is no non-adaptive algorithm without the knowledge of contention size k admitting latency o(k log k/(log log k)2). This means, in particular, that coding (even random) with acknowledgements is not very efficient on a shared channel without synchronization or an estimate of the contention size. We also present a non-adaptive algorithm with no knowledge of contention size that almost matches the lower bound on latency. Finally, despite the absence of a collision de

关键词： adaptive algorithms

Faster adaptive Federated Learning

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arXiv 2022年

作者： Wu, Xidong Huang, Feihu Hu, Zhengmian Huang, Heng Electrical and Computer Engineering University of Pittsburgh PittsburghPA United States College of Computer Science and Technology Nanjing University of Aeronautics and Astronautics Nanjing China

Federated learning has attracted increasing attention with the emergence of distributed data. While extensive federated learning algorithms have been proposed for the non-convex distributed problem, federated learning in practice still faces numerous challenges, such as the large training iterations to converge since the sizes of models and datasets keep increasing, and the lack of adaptivity by SGD-based model updates. Meanwhile, the study of adaptive methods in federated learning is scarce and existing works either lack a complete theoretical convergence guarantee or have slow sample complexity. In this paper, we propose an efficient adaptive algorithm (i.e., FAFED) based on the momentum-based variance-reduced technique in cross-silo FL. We first explore how to design the adaptive algorithm in the FL setting. By providing a counter-example, we prove that a simple combination of FL and adaptive methods could lead to divergence. More importantly, we provide a convergence analysis for our method and prove that our algorithm is the first adaptive FL algorithm to reach the best-known samples O(∊−3) and O(∊−2) communication rounds to find an ∊-stationary point without large batches. The experimental results on the language modeling task and image classification task with heterogeneous data demonstrate the efficiency of our algorithms. Copyright © 2022, The Authors. All rights reserved.

关键词： adaptive algorithms

A projection-based reduced-order model for parametric quasi-static nonlinear mechanics using an open-source industrial code

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arXiv 2022年

作者： Agouzal, Eki Argaud, Jean-Philippe Bergmann, Michel Ferté, Guilhem Taddei, Tommaso EDF Lab Paris-Saclay EDF R&D 7 Boulevard Gaspard Monge Palaiseau91120 France IMB UMR 5251 Univ. Bordeaux Talence33400 France INRIA Inria Bordeaux Sud-Ouest Team MEMPHIS Univ. Bordeaux Talence33400 France

We propose a projection-based model order reduction procedure for a general class of parametric quasi-static problems in nonlinear mechanics with internal variables. The methodology is integrated in the industrial finite element code code aster. Model order reduction aims to lower the computational cost of engineering studies that involve the simulation to a costly high-fidelity differential model for many different parameters, which correspond, for example to material properties or initial and boundary conditions. We develop an adaptive algorithm based on a POD-Greedy strategy, and we develop an hyper-reduction strategy based on an element-wise empirical quadrature in order to speed up the assembly costs of the reduced-order model by building an appropriate reduced mesh. We introduce a cost-efficient error indicator which relies on the reconstruction of the stress field by a Gappy-POD strategy. We present numerical results for a three-dimensional elastoplastic system in order to illustrate and validate the methodology. © 2022, CC BY-NC-SA.

关键词： adaptive algorithms

A New Dual Backward Affine Projection Algorithm for Blind adaptive Acoustic Noise Cancellation

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SSRN

SSRN 2022年

作者： Boumegouas, Rahil Djendi, Mohamed

This paper investigates both acoustic noise reduction and speech signal enhancement by adaptive filters. We propose a new Dual Backward Affine Projection Algorithm (DBAPA) and then use it in the Backward Blind Source Separation Structure (BBSS) to deal with very noisy observations. We use the proposed DBAPA algorithm to extract the noise-free speech signal from very noisy observations without prior information about the source signals. The new DBAPA algorithm is tested in different noisy situations and evaluated in terms of several objective criteria, such as the segmental mean square error (SegMSE), the segmental signal to noise ratio (SegSNR), the system mismatch (SM), and the cepstral distance (CD). The obtained results have shown the good behavior of the proposed DBAPA algorithm in comparison with the classical Dual Backward Normalized Least Mean Square (DBNLMS) algorithm. © 2022, The Authors. All rights reserved.

关键词： adaptive algorithms

An adaptive wavelet method for nonlinear partial differential equations with applications to dynamic damage modeling

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arXiv 2022年

作者： Harnish, Cale Dalessandro, Luke Matouš, Karel Livescu, Daniel Department of Aerospace and Mechanical Engineering University of Notre Dame Notre DameIN46556 United States Department of Intelligent Systems Engineering Indiana University BloomingtonIN47405 United States Computer and Computational Sciences Division Los Alamos National Laboratory Los AlamosNM87545 United States

Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential equations (PDEs) while resolving features on a wide range of spatial and temporal scales. The algorithm exploits the multiresolution nature of wavelet basis functions to solve initial-boundary value problems on finite domains with a sparse multiresolution spatial discretization. By leveraging wavelet theory and embedding a predictor-corrector procedure within the time advancement loop, we dynamically adapt the computational grid and maintain accuracy of the solutions of the PDEs as they evolve. Consequently, our method provides high fidelity simulations with significant data compression. We present verification of the algorithm and demonstrate its capabilities by modeling high-strain rate damage nucleation and propagation in nonlinear solids using a novel Eulerian-Lagrangian continuum framework. Copyright © 2022, The Authors. All rights reserved.

关键词： adaptive algorithms

SECLEDS: Sequence Clustering in Evolving Data Streams via Multiple Medoids and Medoid Voting

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arXiv 2022年

作者： Nadeem, Azqa Verwer, Sicco Delft University of Technology Netherlands

Sequence clustering in a streaming environment is challenging because it is computationally expensive, and the sequences may evolve over time. K-medoids or Partitioning Around Medoids (PAM) is commonly used to cluster sequences since it supports alignment-based distances, and the k-centers being actual data items helps with cluster interpretability. However, offline k-medoids has no support for concept drift, while also being prohibitively expensive for clustering data streams. We therefore propose SECLEDS, a streaming variant of the k-medoids algorithm with constant memory footprint. SECLEDS has two unique properties: i) it uses multiple medoids per cluster, producing stable high-quality clusters, and ii) it handles concept drift using an intuitive Medoid Voting scheme for approximating cluster distances. Unlike existing adaptive algorithms that create new clusters for new concepts, SECLEDS follows a fundamentally different approach, where the clusters themselves evolve with an evolving stream. Using real and synthetic datasets, we empirically demonstrate that SECLEDS produces high-quality clusters regardless of drift, stream size, data dimensionality, and number of clusters. We compare against three popular stream and batch clustering algorithms. The state-of-the-art BanditPAM is used as an offline benchmark. SECLEDS achieves comparable F1 score to BanditPAM while reducing the number of required distance computations by 83.7%. Importantly, SECLEDS outperforms all baselines by 138.7% when the stream contains drift. We also cluster real network traffic, and provide evidence that SECLEDS can support network bandwidths of up to 1.08 Gbps while using the (expensive) dynamic time warping distance. © 2022, CC BY.

关键词： adaptive algorithms