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HETEROGENEOUS MULTISCALE METHODS FOR FOURTH-ORDER SINGULAR PERTURBATIONS

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arXiv 2025年

作者： Liao, Yulei Ming, Pingbing Department of Mathematics Faculty of Science National University of Singapore 10 Lower Kent Ridge Road Singapore119076 Singapore LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

We develop a numerical homogenization method for fourth-order singular perturbation problems within the framework of heterogeneous multiscale method. These problems arise from heterogeneous strain gradient elasticity and elasticity models for architectured materials. We establish an error estimate for the homogenized solution applicable to general media and derive an explicit convergence for the locally periodic media with the fine-scale Ε. For cell problems of size δ = NΕ, the classical resonance error O(Ε/δ) can be eliminated due to the dominance of the higher-order operator. Despite the occurrence of boundary layer effects, discretization errors do not necessarily deteriorate for general boundary conditions. Numerical simulations corroborate these theoretical findings. Copyright © 2025, The Authors. All rights reserved.

关键词： Convergence of numerical methods

Max-Min Fairness in IRS-Aided Multi-Cell MISO Systems with Joint Transmit and Reflective Beamforming

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arXiv 2020年

作者： Xie, Hailiang Xu, Jie Liu, Ya-Feng School of Information Engineering Guangdong University of Technology Guangzhou510006 China Shenzhen518172 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

This paper investigates an intelligent reflecting surface (IRS)-aided multi-cell multiple-input single-output (MISO) system with a set of multi-antenna base stations (BSs) each communicating with a single-antenna user, in which an IRS is dedicatedly deployed for assisting the wireless transmission and suppressing the inter-cell interference. Under this setup, we jointly optimize the coordinated transmit beamforming vectors at the BSs and the reflective beamforming vector at the IRS, for the purpose of maximizing the minimum weighted signal-to-interference-plus-noise ratio (SINR) at the users, subject to the individual maximum transmit power constraints at the BSs and the reflection constraints at the IRS. To solve the non-convex min-weighted-SINR maximization problem, we first present an exact-alternating-optimization approach to optimize the transmit and reflective beamforming vectors in an alternating manner, in which the transmit and reflective beamforming optimization subproblems are solved exactly in each iteration by using the techniques of second-order-cone program (SOCP) and semi-definite relaxation (SDR), respectively. However, the exact-alternating-optimization approach has high computational complexity, and may lead to compromised performance due to the uncertainty of randomization in SDR. To avoid these drawbacks, we further propose an inexact-alternating-optimization approach, in which the transmit and reflective beamforming optimization subproblems are solved inexactly in each iteration based on the principle of successive convex approximation (SCA). In addition, to further reduce the computational complexity, we propose a low-complexity inexact-alternating-optimization design, in which the reflective beamforming optimization subproblem is solved more inexactly. Via numerical results, it is shown that the proposed three designs achieve significantly increased min-weighted-SINR values, as compared with benchmark schemes without the IRS or with random re

关键词： Beamforming

Convergence rate of inertial forward-backward splitting algorithms based on the local error bound condition

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arXiv 2020年

作者： Liu, Hongwei Wang, Ting Liu, Zexian School Of Mathematics And Statistics Xidian University Xi'An710126 China State Key Laboratory Of Scientific And Engineering Computing Institute Of Computational Mathematics And Scientific/Engineering Computing AMSS Chinese Academy Of Sciences Beijing100190 China School Of Mathematics And Statistics Guizhou University Guiyang550025 China

The " Inertial Forward-Backward algorithm " (IFB) is a powerful tool for convex nonsmooth minimization problems, and under the local error bound condition, the R-linear convergence rates for the sequences of objective values and iterates have been proved if the inertial parameter γksatisfies supkγkkγk= 1 is not know. In this paper, based on the local error bound condition, we exploit a new assumption condition for the important parameter tkin IFB, which implies that limk→∞γk= 1, and establish the convergence rate of function values and strong convergence of the iterates generated by the IFB algorithms with six tksatisfying the above assumption condition in Hilbert space. It is remarkable that, under the local error bound condition, we show that the IFB algorithms with some tkcan achieve sublinear convergence rate of o(1/kp) for any positive integer p > 1. In addition, we propose a class of Inertial Forward-Backward algorithm with adaptive modification and show it has same convergence results as IFB under the error bound condition. Some numerical experiments are conducted to illustrate our results. Copyright © 2020, The Authors. All rights reserved.

关键词： Parameter estimation

Distribution system voltage prediction from smart inverters using decentralized regression

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arXiv 2021年

作者： Atkins, Zachary R. Vogl, Christopher J. Madduri, Achintya Duan, Nan Miedlar, Agnieszka K. Merl, Daniel Department of Mathematics University of Kansas Lawrence United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory Livermore United States Computational Engineering Division Lawrence Livermore National Laboratory Livermore United States

As photovoltaic (PV) penetration continues to rise and smart inverter functionality continues to expand, smart inverters and other distributed energy resources (DERs) will play increasingly important roles in distribution system power management and security. In this paper, it is demonstrated that a constellation of smart inverters in a simulated distribution circuit can enable precise voltage predictions using an asynchronous and decentralized prediction algorithm. Using simulated data and a constellation of 15 inverters in a ring communication topology, the COLA algorithm is shown to accomplish the learning task required for voltage magnitude prediction with far less communication overhead than fully connected P2P learning protocols. Additionally, a dynamic stopping criterion is proposed that does not require a regularizer like the original COLA stopping criterion. Copyright © 2021, The Authors. All rights reserved.

关键词： Smart power grids

What we should learn from pandemic publishing

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arXiv 2024年

作者： Sikdar, Satyaki Venturini, Sara Charpignon, Marie-Laure Kumar, Sagar Rinaldi, Francesco Tudisco, Francesco Fortunato, Santo Majumder, Maimuna S. Luddy School of Informatics Computing and Engineering Indiana University BloomingtonIN United States Department of Computer Science Loyola University Chicago ChicagoIL United States Senseable City Laboratory Massachusetts Institute of Technology CambridgeMA United States Department of Mathematics "Tullio Levi-Civita" University of Padova Padova Italy Institute for Data Systems and Society Massachusetts Institute of Technology CambridgeMA United States Network Science Institute Northeastern University BostonMA United States School of Mathematics The University of Edinburgh Edinburgh United Kingdom School of Mathematics Gran Sasso Science Institute L’Aquila Italy Department of Pediatrics Harvard Medical School BostonMA United States Computational Health Informatics Program Boston Children’s Hospital BostonMA United States

Since the emergence of COVID-19, discussions of ongoing pandemic-related research have accounted for an unprecedented share of media coverage and debate in the public sphere1. The urgency of the pandemic forced researchers to operate on an accelerated timeline, as both policymakers and the public relied on the most current evidence to guide their decisions and behaviors. With high demand for rapid pandemic-related insights and lower barriers to entry via preprint servers, the volume of COVID-19 articles skyrocketed2. The pressing need for research triggered the participation of many researchers with expertise in the science of infectious disease outbreaks (‘outbreak scientists’), who were joined by researchers from other disciplines (‘bellwethers’) and more junior researchers still in training (‘newcomers’) with the common goal of advancing the frontiers of pandemic science and informing policy decisions3. Please see Box 1 for details of this taxonomy. © 2024, CC BY-NC-ND.

关键词： COVID-19

Personalized and uncertainty-aware coronary hemodynamics simulations: From Bayesian estimation to improved multi-fidelity uncertainty quantification

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arXiv 2024年

作者： Menon, Karthik Zanoni, Andrea Khan, Owais Geraci, Gianluca Nieman, Koen Schiavazzi, Daniele E. Marsden, Alison L. Stanford School of Medicine StanfordCA United States Institute for Computational and Mathematical Engineering Stanford University StanfordCA United States Department of Electrical Computer and Biomedical Engineering Toronto Metropolitan University TorontoON Canada Center for Computing Research Sandia National Laboratories AlbuquerqueNM United States Division of Cardiovascular Medicine Stanford School of Medicine StanfordCA United States Department of Radiology Stanford School of Medicine StanfordCA United States Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN United States Department of Bioengineering Stanford University StanfordCA United States

Background: Non-invasive simulations of coronary hemodynamics have improved clinical risk stratification and treatment outcomes for coronary artery disease, compared to relying on anatomical imaging alone. However, simulations typically use empirical approaches to distribute total coronary flow amongst the arteries in the coronary tree, which ignores patient variability, the presence of disease, and other clinical factors. Further, uncertainty in the clinical data often remains unaccounted for in the modeling pipeline. Objective: We present an end-to-end uncertainty-aware pipeline to (1) personalize coronary flow simulations by incorporating vessel-specific coronary flows as well as cardiac function;and (2) predict clinical and biomechanical quantities of interest with improved precision, while accounting for uncertainty in the clinical data. Methods: We assimilate patient-specific measurements of myocardial blood flow from clinical CT myocardial perfusion imaging to estimate branch-specific coronary artery flows. Simulated noise in the clinical data is used to estimate the joint posterior distributions of the model parameters using adaptive Markov Chain Monte Carlo sampling. Additionally, the posterior predictive distribution for the relevant quantities of interest is determined using a new approach combining multi-fidelity Monte Carlo estimation with non-linear, data-driven dimensionality reduction. This leads to improved correlations between high- and low-fidelity model outputs. Results: Our framework accurately recapitulates clinically measured cardiac function as well as branch-specific coronary flows under measurement noise uncertainty. We observe substantial reductions in confidence intervals for estimated quantities of interest compared to single-fidelity Monte Carlo estimation and state-of-the-art multi-fidelity Monte Carlo methods. This holds especially true for quantities of interest that showed limited correlation between the low- and high-fidelity model

关键词： Monte Carlo methods

Survey of physics reasoning on uncertainty concepts in experiments: An assessment of measurement uncertainty for introductory physics labs

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Physical Review Physics Education Research 2023年第2期19卷 020139-020139页

作者： Michael Vignal Gayle Geschwind Benjamin Pollard Rachel Henderson Marcos D. Caballero H. J. Lewandowski JILA National Institute of Standards and Technology and the University of Colorado Boulder Colorado 80309 USA Department of Physics University of Colorado 390 UCB Boulder Colorado 80309 USA Department of Physics Worcester Polytechnic Institute 100 Institute Road Worcester Massachusetts 01609 USA Department of Physics & Astronomy and CREATE for STEM Institute Michigan State University East Lansing Michigan 48824 USA Department of Computational Mathematics Science & Engineering Michigan State University East Lansing Michigan 48824 USA Department of Physics and Center for Computing in Science Education University of Oslo 0315 Oslo Norway

[This paper is part of the Focused Collection on Instructional labs: Improving traditions and new directions.] Measurement uncertainty is a critical feature of experimental research in the physical sciences, and the concepts and practices surrounding measurement uncertainty are important components of physics lab courses. However, there has not been a broadly applicable, research-based assessment tool that allows physics instructors to easily measure students’ knowledge of measurement uncertainty concepts and practices. To address this need, we employed evidence-centered design to create the Survey of Physics Reasoning on Uncertainty Concepts in Experiments (SPRUCE). SPRUCE is a pre-post assessment instrument intended for use in introductory (first and second year) physics lab courses to help instructors and researchers identify student strengths and challenges with measurement uncertainty. In this paper, we discuss the development of SPRUCE’s assessment items guided by evidence-centered design, focusing on how instructors’ and researchers’ assessment priorities were incorporated into the assessment items and how students’ reasoning from pilot testing informed decisions around item answer options. We also present an example of some of the feedback an instructor would receive after implementing SPRUCE in a pre-post fashion, along with a brief discussion of how that feedback could be interpreted and acted upon.

关键词： Assessment Lower undergraduate students

Cramér-rao bound optimization for joint radar-communication design

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arXiv 2021年

作者： Liu, Fan Liu, Ya-Feng Li, Ang Masouros, Christos Eldar, Yonina C. The Department of Electrical and Electronic Engineering Southern University of Science and Technology Shenzhen518055 China The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematicsand Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China The School of Information and Communications Engineering Faculty of Electronic and Information Engineering Xi’an Jiaotong University Xi’anShaanxi710049 China The Department of Electronic and Electrical Engineering University College London LondonWC1E 7JE United Kingdom The Faculty of Mathematics and Computer Science Weizmann Institute of Science Rehovot Israel

In this paper, we propose multi-input multi-output (MIMO) beamforming designs towards joint radar sensing and multi-user communications. We employ the Cramér-Rao bound (CRB) as a performance metric of target estimation, under both point and extended target scenarios. We then propose minimizing the CRB of radar sensing while guaranteeing a pre-defined level of signal-to-interference-plus-noise ratio (SINR) for each communication user. For the single-user scenario, we derive a closed form for the optimal solution for both cases of point and extended targets. For the multi-user scenario, we show that both problems can be relaxed into semidefinite programming by using the semidefinite relaxation approach, and prove that the global optimum can always be obtained. Finally, we demonstrate numerically that the globally optimal solutions are reachable via the proposed methods, which provide significant gains in target estimation performance over state-of-the-art benchmarks. Copyright © 2021, The Authors. All rights reserved.

关键词： Signal to noise ratio

Accelerating Matrix Diagonalization through Decision Transformers with Epsilon-Greedy Optimization

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arXiv 2024年

作者： Bhatta, Kshitij Zollicoffer, Geigh Bhattarai, Manish Romero, Phil Negre, Christian F.A. Niklasson, Anders M.N. Adedoyin, Adetokunbo Department of Mechanical and Aerospace Engineering University of Virginia CharlottesvilleVA22904 United States School of Mathematics Georgia Institute of Technology AtlantaGA30332 United States High Performance Computing Division Los Alamos National Laboratory NM87545 United States Theoretical Division Los Alamos National Laboratory NM87545 United States Computational Science Division Los Alamos National Laboratory NM87545 United States

This paper introduces a novel framework for matrix diagonalization, recasting it as a sequential decision-making problem and applying the power of Decision Transformers (DTs). Our approach determines optimal pivot selection during diagonalization with the Jacobi algorithm, leading to significant speedups compared to the traditional max-element Jacobi method. To bolster robustness, we integrate an epsilon-greedy strategy, enabling success in scenarios where deterministic approaches fail. This work demonstrates the effectiveness of DTs in complex computational tasks and highlights the potential of reimagining mathematical operations through a machine learning lens. Furthermore, we establish the generalizability of our method by using transfer learning to diagonalize matrices of smaller sizes than those trained. Copyright © 2024, The Authors. All rights reserved.

关键词： Reinforcement learning