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Hashing embeddings of optimal dimension, with applications to linear least squares

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arXiv 2021年

作者： Cartis, Coralia Fiala, Jan Shao, Zhen Mathematical Institute University of Oxford Radcliffe Observatory Quarter Woodstock Road OxfordOX2 6GG United Kingdom Numerical Algorithms Group Ltd 30 St Giles OxfordOX1 3LE United Kingdom

The aim of this paper is two-fold: firstly, to present subspace embedding properties for s-hashing sketching matrices, with s ≥ 1, that are optimal in the projection dimension m of the sketch, namely, m = O(d), where d is the dimension of the subspace. A diverse set of results are presented that address the case when the input matrix has sufficiently low coherence (thus removing the log2 d factor dependence in m, in the low-coherence result of Bourgain et al (2015) at the expense of a smaller coherence requirement);how this coherence changes with the number s of column nonzeros (allowing a scaling of √s of the coherence bound), or is reduced through suitable transformations (when considering hashed-instead of subsampled- coherence reducing transformations such as randomised Hadamard). Secondly, we apply these general hashing sketching results to the special case of Linear Least Squares (LLS), and develop Ski-LLS, a generic software package for these problems, that builds upon and improves the Blendenpik solver on dense input and the (sequential) LSRN performance on sparse problems. In addition to the hashing sketching improvements, we add suitable linear algebra tools for rank-deficient and for sparse problems that lead SkiLLS to outperform not only sketching-based routines on randomly generated input, but also state of the art direct solver SPQR and iterative code HSL on certain subsets of the sparse Florida matrix collection;namely, on least squares problems that are significantly overdetermined, or moderately sparse, or *** Codes 65K05, 93E24, 65F08, 65F10, 65F20, 65F50, 62J05 © 2021, CC BY.

关键词： Iterative methods

DECICE: Device-Edge-Cloud Intelligent Collaboration Framework

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arXiv 2023年

作者： Kunkel, Julian Boehme, Christian Decker, Jonathan Magugliani, Fabrizio Pleiter, Dirk Koller, Bastian Sivalingam, Karthee Pllana, Sabri Nikolov, Alexander Soyturk, Mujdat Racca, Christian Bartolini, Andrea Tate, Adrian Yaman, Berkay Universität Göttingen Göttingen Germany GWDG Göttingen Germany E4 Computer Engineering S.p.A. Scandiano Italy KTH Royal Institute of Technology Stockholm Sweden HLRS Stuttgart Germany Huawei Technologies Düsseldorf GmbH Düsseldorf Germany Forschung Burgenland GmbH Eisenstadt Austria SYNYO GmbH Wien Austria Marmara University Istanbul Turkey Consorzio TOP-IX Torino Italy Alma Mater Studiorum - Università di Bologna Bologna Italy Numerical Algorithms Group Limited Oxford United Kingdom BigTRI Bilisim A.S. Istanbul Turkey

DECICE is a Horizon Europe project that is developing an AI-enabled open and portable management framework for automatic and adaptive optimization and deployment of applications in computing continuum encompassing from IoT sensors on the Edge to large-scale Cloud/HPC computing infrastructures. In this paper, we describe the DECICE framework and architecture. Furthermore, we highlight use-cases for framework evaluation: intelligent traffic intersection, magnetic resonance imaging, and emergency response. © 2023, CC BY.

关键词： Magnetic resonance imaging

Enabling System Wide Shared Memory for Performance Improvement in PyCOMPSs Applications

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Enabling System Wide Shared Memory for Performance Improveme...

Workshop on Python for High-Performance and Scientific Computing (PyHPC)

作者： Clément Foyer Javier Conejero Jorge Ejarque Rosa M. Badia Adrian Tate Simon McIntosh-Smith HPE HPC/AI EMEA Research Lab Bristol United Kingdom High Performance Computing Research Group University of Bristol Bristol United Kingdom Barcelona Supercomputing Center Barcelona Spain Numerical Algorithms Group Ltd. (NAG) Oxford United Kingdom

ISBN: (数字)9780738110868

ISBN: (纸本)9781665422864

Python has been gaining some traction for years in the world of scientific applications. However, the high-level abstraction it provides may not allow the developer to use the machines to their peak performance. To address this, multiple strategies, sometimes complementary, have been developed to enrich the software ecosystem either by relying on additional libraries dedicated to efficient computation (e.g., NumPy) or by providing a framework to better use HPC scale infrastructures (e.g., PyCOMPSs).In this paper, we present a Python extension based on SharedArray that enables the support of system-provided shared memory and its integration into the PyCOMPSs programming model as an example of integration to a complex Python environment. We also evaluate the impact such a tool may have on performance in two types of distributed execution-flows, one for linear algebra with a blocked matrix multiplication application and the other in the context of data-clustering with a k-means application. We show that with very little modification of the original decorator (3 lines of code to be modified) of the task-based application the gain in performance can rise above 40% for tasks relying heavily on data reuse on a distributed environment, especially when loading the data is prominent in the execution time.

关键词： Task analysis Python Memory management Runtime Libraries Tools Metadata

Modelling binary alloy solidification with adaptive mesh refinement

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Journal of Computational Physics: X 2020年 5卷

作者： Parkinson, James R.G. Martin, Daniel F. Wells, Andrew J. Katz, Richard F. Atmospheric Oceanic and Planetary Physics Department of Physics Clarendon Laboratory University of Oxford Parks Road OxfordOX1 3PU United Kingdom Applied Numerical Algorithms Group Lawrence Berkeley National Laboratory BerkeleyCA United States Department of Earth Sciences University of Oxford South Parks Road OxfordOX1 3AN United Kingdom

The solidification of a binary alloy results in the formation of a porous mushy layer, within which spontaneous localisation of fluid flow can lead to the emergence of features over a range of spatial scales. We describe a finite volume method for simulating binary alloy solidification in two dimensions with local mesh refinement in space and time. The coupled heat, solute, and mass transport is described using an enthalpy method with flow described by a Darcy-Brinkman equation for flow across porous and liquid regions. The resulting equations are solved on a hierarchy of block-structured adaptive grids. A projection method is used to compute the fluid velocity, whilst the viscous and nonlinear diffusive terms are calculated using a semi-implicit scheme. A series of synchronization steps ensure that the scheme is flux-conservative and correct for errors that arise at the boundaries between different levels of refinement. We also develop a corresponding method using Darcy's law for flow in a porous medium/narrow Hele-Shaw cell. We demonstrate the accuracy and efficiency of our method using established benchmarks for solidification without flow and convection in a fixed porous medium, along with convergence tests for the fully coupled code. Finally, we demonstrate the ability of our method to simulate transient mushy layer growth with narrow liquid channels which evolve over time. © 2019

关键词： Binary alloys

High performance computing evaluate and plan 18

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High performance computing evaluate and plan

2018 Practice and Experience in Advanced Research Computing Conference: Seamless Creativity, PEARC 2018

作者： Eicher, Beth Lynn Solomon, Steven Hall, Shawn Arcutek Corporation 73 West Monroe Street ChicagoIL60615 United States Numerical Algorithms Group 801 Warrenville Rd # 185 LisleIL60532 United States

ISBN: (纸本)9781450364461

Arcutek will develop a security service called "HEAP" or "HPC Evaluation And Plan" as a complete configuration of security solutions for connection, file ingress/egress, compute, data-at-rest and other infrastructure areas. Security for HPC environments is complex and requires a holistic approach to identify, protect, detect, respond and recover from security events. Some vendor-specific guides are available through the National Institute of Standards and Technology and the Center for Internet Security, but no government or industry plan completely encompasses the security of HPC architecture. We endeavor to research common off the shelf products and open source tools which would bring HPC components into compliance with the NIST 800-53A Revision 4 and the "Security Controls Catalog and Assessment Procedures."[1]. © 2018 Copyright is held by the owner/author(s).

关键词： Compliance control

Improving the flexibility and robustness of model-based derivative-free optimization solvers

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arXiv 2018年

作者： Cartis, Coralia Fiala, Jan Marteau, Benjamin Roberts, Lindon Mathematical Institute University of Oxford Radcliffe Observatory Quarter Woodstock Road OxfordOX2 6GG United Kingdom Numerical Algorithms Group Wilkinson House Jordan Hill Road OxfordOX2 8DR United Kingdom Numerical Algorithms Group Wilkinson House Jordan Hill Road OxfordOX2 8DR United Kingdom Mathematical Institute University of Oxford Radcliffe Observatory Quarter Woodstock Road OxfordOX2 6GG United Kingdom

We present DFO-LS, a software package for derivative-free optimization (DFO) for nonlinear Least-Squares (LS) problems, with optional bound constraints. Inspired by the Gauss-Newton method, DFO-LS constructs simplified linear regression models for the residuals. DFO-LS allows flexible initialization for expensive problems, whereby it can begin making progress from as few as two objective evaluations. numerical results show DFO-LS can gain reasonable progress on some medium-scale problems with fewer objective evaluations than is needed for one gradient evaluation. DFO-LS has improved robustness to noise, allowing sample averaging, the construction of regression-based models, and multiple restart strategies together with an auto-detection mechanism. Our extensive numerical experimentation shows that restarting the solver when stagnation is detected is a cheap and effective mechanism for achieving robustness, with superior performance over both sampling and regression techniques. We also present our package Py-BOBYQA, a Python implementation of BOBYQA (Powell, 2009), which also implements robustness to noise strategies. Our numerical experiments show that Py-BOBYQA is comparable to or better than existing general DFO solvers for noisy problems. In our comparisons, we introduce a new adaptive measure of accuracy for the data profiles of noisy functions that strikes a balance between measuring the true and the noisy objective improvement. Copyright © 2018, The Authors. All rights reserved.

关键词： Python

Ten simple rules for measuring the impact of workshops

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PLoS Computational Biology 2018年第8期14卷 e1006191-e1006191页

作者： Sufi, Shoaib Nenadic, Aleksandra Silva, Raniere Duckles, Beth Simera, Iveta de Beyer, Jennifer A. Struthers, Caroline Nurmikko-Fuller, Terhi Bellis, Louisa Miah, Wadud Wilde, Adriana Emsley, Iain Philippe, Olivier Balzano, Melissa Coelho, Sara Ford, Heather Jones, Catherine Higgins, Vanessa School of Computer Science University of Manchester Manchester United Kingdom Portland State University PortlandOR United States UK EQUATOR Centre Centre for Statistics in Medicine Nuffield Department of Orthopaedics Rheumatology Musculoskeletal Sciences University of Oxford Oxford United Kingdom College of Arts and Social Sciences Australian National University Canberra Australia Cancer Research UK Cambridge Centre University of Cambridge Cambridge United Kingdom Numerical Algorithms Group Oxford United Kingdom School of Computer Science University of St. Andrews St. Andrews United Kingdom Oxford e-Research Centre University of Oxford Oxford United Kingdom Electronics and Computer Science University of Southampton Southampton United Kingdom ELIXIR Hub Wellcome Genome Campus Cambridge United Kingdom EGI Foundation Amsterdam Netherlands School of Media and Communication University of Leeds Leeds United Kingdom Scientific Computing Department Science and Technology Facilities Council Rutherford Appleton Laboratory Didcot United Kingdom School of Social Sciences University of Manchester Manchester United Kingdom

Workshops are used to explore a specific topic, to transfer knowledge, to solve identified problems, or to create something new. In funded research projects and other research endeavours, workshops are the mechanism used to gather the wider project, community, or interested people together around a particular topic. However, natural questions arise: how do we measure the impact of these workshops? Do we know whether they are meeting the goals and objectives we set for them? What indicators should we use? In response to these questions, this paper will outline rules that will improve the measurement of the impact of workshops. © 2018 Sufi et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

关键词： Computer programming

Performance optimisation and productivity centre of excellence

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Performance optimisation and productivity centre of excellen...

International Conference on High Performance Computing & Simulation (HPCS)

作者： Sally Bridgwater Numerical Algorithms Group Oxford UK

As machines get larger and scientific applications advance, it is more and more imperative to fully utilize high performance computing (HPC) capability. The complexity and changing landscape of parallel computers may lead to users being unable or unsure how to achieve optimal performance from their applications and fully utilize their HPC resources. The Performance Optimisation and Productivity Centre of Excellence in Computing Applications (POP) has received funding from the European Commission as part of the Horizon 2020 programme to help alleviate these issues. It aims to uncover inefficiencies and their causes in existing parallel HPC applications that will lead to an improvement in the productivity and competitiveness of European organizations, in academia, government and industry. The POP project will drive efforts to highlight the need for and best practices in performance optimization through performance audits on codes along with training events to improve knowledge in this area. The aim is to help developers target their code development and refactoring in the most efficient direction and provide a return on investment from the savings due to the performance improvement. The POP project combines the expertise and experience of Barcelona Supercomputing Center (BSC), High Performance Computing Center Stuttgart, Jülich Supercomputing Centre (JSC), numerical algorithms group Ltd (NAG), RWTH Aachen and TERATEC. This combination provides longstanding and well respected resources in the academic and commercial realms. The POP members have come together to create a coherent and consistent methodology to give a clear, precise and useful overview of the performance of each HPC application. The services of the POP project are free of charge to organizations with in the EU to analyze and advise on any parallel code in academic, government or industrial organizations of any domain.

关键词： Optimization Productivity Europe Organizations High performance computing Performance analysis Scalability

A moving control volume approach to computing hydrodynamic forces and torques on immersed bodies

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arXiv 2017年

作者： Nangia, Nishant Johansen, Hans Patankar, Neelesh A. Bhalla, Amneet Pal Singh Department of Engineering Sciences and Applied Mathematics Northwestern University EvanstonIL United States Department of Mechanical Engineering Northwestern University EvanstonIL United States Applied Numerical Algorithms Group Lawrence Berkeley National Laboratory BerkeleyCA United States

We present a moving control volume (CV) approach to computing hydrodynamic forces and torques on complex geometries. The method requires surface and volumetric integrals over a simple and regular Cartesian box that moves with an arbitrary velocity to enclose the body at all times. The moving box is aligned with Cartesian grid faces, which makes the integral evaluation straightforward in an immersed boundary (IB) framework. Discontinuous and noisy derivatives of velocity and pressure at the uid-structure interface are avoided and far-field (smooth) velocity and pressure information is used. We re-visit the approach to compute hydrodynamic forces and torques through force/torque balance equation in a Lagrangian frame that some of us took in a prior work (Bhalla et al., J Comp Phys, 2013). We prove the equivalence of the two approaches for IB methods, thanks to the use of Peskin's delta functions. Both approaches are able to suppress spurious force oscillations and are in excellent agreement, as expected theoretically. Test cases ranging from Stokes to high Reynolds number regimes are considered. We discuss regridding issues for the moving CV method in an adaptive mesh refinement (AMR) context. The proposed moving CV method is not limited to a specific IB method and can also be used, for example, with embedded boundary methods. Copyright © 2017, The Authors. All rights reserved.

关键词： Lagrange multipliers