检索结果-内蒙古大学图书馆

arXiv 2020年

作者： Leea, Chak Shing Hamon, Francois Castelletto, Nicola Vassilevski, Panayot S. White, Joshua Center for Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA94550 United States Total EandP Research and Technology HoustonTX77002 United States Atmospheric Earth and Energy Division Lawrence Livermore National Laboratory LivermoreCA94550 United States Department of Energy Resources Engineering Stanford University StanfordCA94305 United States Fariborz Maseeh Department of Mathematics and Statistics Portland State University PortlandOR97201 United States

This work develops a nonlinear multigrid method for difiusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is constructed algebraically using aggregation of degrees of freedom and spectral decomposition of reference linear operators associated with the aggregates. For rapid convergence, it is important that the resulting coarse spaces have good approximation properties. In our approach, the approximation quality can be directly improved by including more spectral degrees of freedom in the coarsening process. Further, by exploiting local coarsening and a piecewise-constant approximation when evaluating the nonlinear component, the coarse level problems are assembled and solved without ever re-visiting the fine level, an essential element for multigrid algorithms to achieve optimal scalability. Numerical examples comparing relative performance of the proposed nonlinear multigrid solvers with standard single-level approaches-Picard's and Newton's methods-are presented. Results show that the proposed solver consistently outperforms the single-level methods, both in effciency and robustness. Copyright © 2020, The Authors. All rights reserved.

关键词： Finite volume method

来源：评论

学校读者我要写书评

暂无评论

Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AI 41

Position: Bayesian Deep Learning is Needed in the Age of Lar...

引用

41st International Conference on Machine Learning, ICML 2024

作者： Papamarkou, Theodore Skoularidou, Maria Palla, Konstantina Aitchison, Laurence Arbel, Julyan Dunson, David Filippone, Maurizio Fortuin, Vincent Hennig, Philipp Hernández-Lobato, José Miguel Hubin, Aliaksandr Immer, Alexander Karaletsos, Theofanis Khan, Mohammad Emtiyaz Kristiadi, Agustinus Li, Yingzhen Mandt, Stephan Nemeth, Christopher Osborne, Michael A. Rudner, Tim G.J. Rügamer, David Teh, Yee Whye Welling, Max Wilson, Andrew Gordon Zhang, Ruqi Department of Mathematics The University of Manchester Manchester United Kingdom Eric and Wendy Schmidt Center Broad Institute of MIT and Harvard Cambridge United States Spotify London United Kingdom Computational Neuroscience Unit University of Bristol Bristol United Kingdom Centre Inria de l'Université Grenoble Alpes Grenoble France Department of Statistical Science Duke University United States Statistics Program KAUST Saudi Arabia Helmholtz AI Munich Germany Department of Computer Science Technical University of Munich Munich Germany Munich Center for Machine Learning Munich Germany Tübingen AI Center University of Tübingen Tübingen Germany Department of Engineering University of Cambridge Cambridge United Kingdom Department of Mathematics University of Oslo Oslo Norway Bioinformatics and Applied Statistics Norwegian University of Life Sciences Ås Norway Department of Computer Science ETH Zurich Switzerland Chan Zuckerberg Initiative CA United States Center for Advanced Intelligence Project RIKEN Tokyo Japan Vector Institute Toronto Canada Department of Computing Imperial College London London United Kingdom Department of Computer Science UC Irvine Irvine United States Department of Mathematics and Statistics Lancaster University Lancaster United Kingdom Department of Engineering Science University of Oxford Oxford United Kingdom Center for Data Science New York University New York United States Department of Statistics LMU Munich Munich Germany DeepMind London United Kingdom Department of Statistics University of Oxford Oxford United Kingdom Informatics Institute University of Amsterdam Amsterdam Netherlands Courant Institute of Mathematical Sciences Center for Data Science Computer Science Department New York University New York United States Department of Computer Science Purdue University West Lafayette United States

In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets. However, a broader perspective reveals a multitude of overlooked metrics, tasks, and data types, such as uncertainty, active and continual learning, and scientific data, that demand attention. Bayesian deep learning (BDL) constitutes a promising avenue, offering advantages across these diverse settings. This paper posits that BDL can elevate the capabilities of deep learning. It revisits the strengths of BDL, acknowledges existing challenges, and highlights some exciting research avenues aimed at addressing these obstacles. Looking ahead, the discussion focuses on possible ways to combine large-scale foundation models with BDL to unlock their full potential. Copyright 2024 by the author(s)

关键词： Contrastive Learning

来源：评论

学校读者我要写书评

暂无评论

Multilevel convergence analysis of multigrid-reduction-in-time

arXiv

引用

arXiv 2018年

作者： HESSENTHALER, ANDREAS SOUTHWORTH, BEN S. NORDSLETTEN, DAVID RÖHRLE, OLIVER FALGOUT, ROBERT D. SCHRODER, JACOB B. Institute for Modelling and Simulation of Biomechanical Systems University of Stuttgart Pfaffenwaldring 5a Stuttgart70565 Germany Department of Applied Mathematics University of Colorado at Boulder CO United States Division of Imaging Sciences and Biomedical Engineering King's College London St. Thomas Hospital 4th Floor Lambeth Wing LondonSE1 7EH United Kingdom Center for Applied Scientific Computing Lawrence Livermore National Laboratory P.O. Box 808 L-561 LivermoreCA94551 United States Department of Mathematics and Statistics University of New Mexico 310 SMLC AlbuquerqueNM87131 United States

This paper presents a multilevel convergence framework for multigrid-reduction-intime (MGRIT) as a generalization of previous two-grid estimates. The framework provides a priori upper bounds on the convergence of MGRIT V- and F-cycles, with different relaxation schemes, by deriving the respective residual and error propagation operators. The residual and error operators are functions of the time stepping operator, analyzed directly and bounded in norm, both numerically and analytically. We present various upper bounds of different computational cost and varying sharpness. These upper bounds are complemented by proposing analytic formulae for the approximate convergence factor of V-cycle algorithms that take the number of fine grid time points, the temporal coarsening factors, and the eigenvalues of the time stepping operator as parameters. The paper concludes with supporting numerical investigations of parabolic (anisotropic diffusion) and hyperbolic (wave equation) model problems. We assess the sharpness of the bounds and the quality of the approximate convergence factors. Observations from these numerical investigations demonstrate the value of the proposed multilevel convergence framework for estimating MGRIT convergence a priori and for the design of a convergent algorithm. We further highlight that observations in the literature are captured by the theory, including that two-level Parareal and multilevel MGRIT with F-relaxation do not yield scalable algorithms and the benefit of a stronger relaxation scheme. An important observation is that with increasing numbers of levels MGRIT convergence deteriorates for the hyperbolic model problem, while constant convergence factors can be achieved for the diffusion equation. The theory also indicates that L-stable Runge-Kutta schemes are more amendable to multilevel parallel-in-time integration with MGRIT than A-stable Runge-Kutta schemes. Copyright © 2018, The Authors. All rights reserved.

关键词： Coarsening

来源：评论

学校读者我要写书评

暂无评论

An improved stopping criterion for anisotropic diffusion

引用

AIP Conference Proceedings 2015年第1期1648卷

作者： Maryam Khanian Michael Breuß Ali Davari *Institute for Applied Mathematics and Scientific Computing Brandenburg University of Technology (BTU) Cottbus-Senftenberg Platz der Deutschen Einheit 1 HG 03046 Cottbus Germany †Department of Mathematics Faculty of Mathematical Sciences and Statistics University of Isfahan Isfahan Iran

Anisotropic diffusion is a time-dependent process in image processing useful for denoising and related tasks. applied at an input image, the latter is gradually simplified in such a way that edges tend to be preserved. Meaningful image structures can then be detected depending on the diffusion time and the spatial scale of a structure. One of the most important points in anisotropic diffusion filtering is introducing a stopping criterion for the time evolution as this defines the quality of output images. In this paper, we follow the approach of a recent method by Ilyevsky and Turkel for determining a useful stopping time. While following the same basic idea, we simplify the underlying algorithm and improve at the same time the quality of filtering results significantly. The superiority of our scheme is validated by several numerical experiments with standard test images in the field.

关键词：

来源：评论

学校读者我要写书评

暂无评论

Potential numerical techniques and challenges for atmospheric modeling

Potential numerical techniques and challenges for atmospheri...

引用

作者： Li, J. Steppeler, J. Fang, F. Pain, C.C. Zhu, J. Peng, X. Dong, L. Li, Y. Tao, L. Leng, W. Wang, Y. Zheng, J. International Center for Climate and Environment Sciences Institute of Atmospheric Physics Chinese Academy of Sciences Beijing China Hamburg Germany Applied Modelling and Computation Group Department of Earth Science and Engineering Imperial College London London United Kingdom International Center for Climate and Environment Sciences Institute of Atmospheric Physics Chinese Academy of Sciences Department of Atmospheric Sciences University of Chinese Academy of Sciences Beijing China State Key Laboratory of Severe Weather Chinese Academy of Meteorological Sciences Beijing China State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Institute of Atmospheric Physics Chinese Academy of Sciences Beijing China State Key Laboratory of Scientific and Engineering Computing Chinese Academy of Sciences Beijing China School of Mathematics and Statistics Henan University Kaifeng China Center for Excellence in Regional Atmospheric Environment Institute of Urban Environment Chinese Academy of Sciences Xiamen China

来源：评论

学校读者我要写书评

暂无评论

Parallelized Domain Decomposition for Multi-Dimensional Lagrangian Random Walk, Mass-Transfer Particle Tracking Schemes

SSRN

引用

SSRN 2022年

作者： Schauer, Lucas Schmidt, Michael J. Engdahl, Nicholas B. Pankavich, Stephen D. Benson, David A. Bolster, Diogo Department of Applied Mathematics and Statistics Colorado School of Mines GoldenCO80401 United States Center for Computing Research Sandia National Laboratories AlbuquerqueNM87185 United States Department of Civil and Environmental Engineering Washington State University PullmanWA99164 United States Hydrologic Science and Engineering Program Department of Geology and Geological Engineering Colorado School of Mines GoldenCO80401 United States Department of Civil and Environmental Engineering and Earth Sciences University of Notre Dame Notre DameIN46556 United States

We develop a multi-dimensional, parallelized domain decomposition strategy (DDC) for mass-transfer particle tracking (MTPT) methods. These methods are a type of Lagrangian algorithm for simulating reactive transport and are able to be parallelized by employing large numbers of CPU cores to accelerate run times. In this work, we investigate different procedures for "tiling" the domain in two and three dimensions, (2-d and 3-d), as this type of formal DDC construction is currently limited to 1-d. An optimal tiling is prescribed based on physical problem parameters and the number of available CPU cores, as each tiling provides distinct results in both accuracy and run time. We further extend the most efficient technique to 3-d for comparison, leading to an analytical discussion of the effect of dimensionality on strategies for implementing DDC schemes. Increasing computational resources (cores) within the DDC method produces a trade-off between inter-node communication and on-node work. For an optimally subdivided diffusion problem, the 2-d parallelized algorithm achieves nearly perfect linear speedup in comparison with the serial run up to around 2700 cores, reducing a 5-hour simulation to 8 seconds, and the 3-d algorithm maintains appreciable speedup up to 1700 cores. © 2022, The Authors. All rights reserved.

关键词： Lagrange multipliers

来源：评论

学校读者我要写书评

暂无评论

Convergence of Mass Transfer Particle Tracking Schemes for the Simulation of Advection-Diffusion-Reaction Equations

SSRN

引用

SSRN 2024年

作者： Pankavich, Stephen D. Schauer, Lucas Schmidt, Michael J. Engdahl, Nicholas B. Bolster, Diogo Benson, David A. Department of Applied Mathematics and Statistics Colorado School of Mines GoldenCO80401 United States Center for Computing Research Sandia National Laboratories AlbuquerqueNM87185 United States Department of Civil and Environmental Engineering Washington State University PullmanWA99164 United States Department of Civil and Environmental Engineering and Earth Sciences University of Notre Dame Notre DameIN46556 United States Hydrologic Science and Engineering Program Department of Geology and Geological Engineering Colorado School of Mines GoldenCO80401 United States

Since their introduction, multi-species mass-transfer particle tracking (or MTPT) algorithms have been used to accurately simulate advective and dispersive transport of solutes, even within systems that feature nonlinear chemical reactions. The MTPT methods were originally derived from a probabilistic or first-principles perspective and have previously lacked a more rigorous derivation arising directly from the underlying advection-diffusion-reaction equation (ADRE). Herein, we provide a fully rigorous derivation of the MTPT method as a Lagrangian approximation of solutions to the ADRE, complete with a description of the error and order of accuracy generated by this approximation. Numerical simulations further detail the fidelity of MTPT methods and display parameter regimes wherein the numerical error is independent of the chosen time step, and thereby dependent only upon the numerical discretization of the spatial domain via the number of particles within a simulation. Finally, different normalizations of the local Green's function are shown to generate similar approximations of the underlying solution for stationary particles. © 2024, The Authors. All rights reserved.

关键词： Lagrange multipliers

来源：评论

学校读者我要写书评

暂无评论

Parallelized Domain Decomposition for Multi-Dimensional Lagrangian Random Walk, Mass-Transfer Particle Tracking Schemes

arXiv

引用

arXiv 2022年

关键词： Lagrange multipliers

来源：评论

学校读者我要写书评

暂无评论

The estimation of the effective reproductive number from disease outbreak data

arXiv

引用

arXiv 2020年

作者： Cintrón-Arias, Ariel Castillo-Chávez, Carlos Bettencourt, Luís M.A. Lloyd, Alun L. Banks, H.T. Statistical and Applied Mathematical Sciences Institute 19 T. W. Alexander Drive P.O. Box 14006 Research Triangle ParkNC27709-4006 United States Department of Mathematics and Statistics Arizona State University P.O. Box 871804 TempeAZ85287 - 1804 Los Alamos National Laboratory Mail Stop B284 Los AlamosNM87545 United States Biomathematics Graduate Program Department of Mathematics North Carolina State University RaleighNC27695 United States Center for Research in Scientific Computation North Carolina State University P.O. Box 8205 RaleighNC27695

We consider a single outbreak susceptible-infected-recovered (SIR) model and corresponding estimation procedures for the effective reproductive number R(t). We discuss the estimation of the underlying SIR parameters with a generalized least squares (GLS) estimation technique. We do this in the context of appropriate statistical models for the measurement process. We use asymptotic statistical theories to derive the mean and variance of the limiting (Gaussian) sampling distribution and to perform post statistical analysis of the inverse problems. We illustrate the ideas and pitfalls (e.g., large condition numbers on the corresponding Fisher information matrix) with both synthetic and influenza incidence data sets. Copyright © 2020, The Authors. All rights reserved.

关键词： Parameter estimation

来源：评论

学校读者我要写书评

暂无评论

A Comparative Study of Gaussian Process Machine Learning and Time Series Analysis Techniques for Predicting Unemployment Rate

A Comparative Study of Gaussian Process Machine Learning and...

引用

International Conference on Computer and Automation Engineering, ICCAE

作者： Muhammad Naeim Mohd Aris Shalini Nagaratnam Nurul Nnadiah Zakaria Muhammad Fadhirul Anuar Mohd Azami Muhammad Afiq Ikram Samsudin Ernee Sazlinayati Othman Department of American Degree Transfer Program School of American Education Sunway University Bandar Sunway Malaysia Department of Econometrics and Business Statistics School of Business Monash University Malaysia Bandar Sunway Malaysia Department of Fundamental and Applied Sciences Faculty of Science and Information Technology Universiti Teknologi PETRONAS Seri Iskandar Malaysia Department of American Degree Transfer Programme School of American Education Sunway University Bandar Sunway Malaysia College of Computing Informatics and Mathematics Universiti Teknologi MARA Seremban 3 Malaysia Centre of Foundation Studies Universiti Teknologi MARA Cawangan Selangor Kampus Dengkil Dengkil Malaysia

ISBN: (数字)9798350370058

ISBN: (纸本)9798350370164

This study explores and compares the capability of Gaussian process machine learning (GPML) with time series analysis techniques, which are autoregressive integrated moving average (ARIMA), seasonal ARIMA (SARIMA) and cubic spline interpolation, in modeling unemployment rate in Malaysia over the period of 1991 to 2022. Six predictive models are developed based on the observations. The predictive performance of each model is quantified using mean absolute error (MAE) and mean squared error (MSE). GPML demonstrated the best predictive model, exhibiting minimal MAE and MSE compared to the time series analysis techniques. The statistical analysis also concluded no significant mean difference between the GPML model and the actual observations, implying a robust predictive model in predicting the unemployment rate in Malaysia.

关键词： Analytical models Interpolation Statistical analysis Time series analysis Gaussian processes Machine learning Predictive models

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：