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Implementation of a scalable, performance portable shallow water equation solver using radial basis function-generated finite difference methods

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INTERNATIONAL JOURNAL OF HIGH PERFORMANCE COMPUTING APPLICATIONS 2019年第4期33卷 619-631页

作者： Elliott, Samuel Kumar, Raghu Raj Prasanna Flyer, Natasha Ta, Tuan Loft, Richard Univ Colorado Appl Math Boulder CO 80309 USA Natl Ctr Atmospher Res Special Tech Projects Grp POB 3000 Boulder CO 80307 USA Natl Ctr Atmospher Res Sci Comp POB 3000 Boulder CO 80307 USA Natl Ctr Atmospher Res Computat & Informat Syst Lab Technol Dev POB 3000 Boulder CO 80307 USA Univ Mississippi Oxford MS USA Natl Ctr Atmospher Res Boulder CO USA

In this article, we describe and analyze the computational performance of a parallel shallow water equation (SWE) solver for atmospheric simulation using radial basis function-finite difference (RBF-FD) methods. The inherent "meshless" nature of RBF-FD methods provides significant numerical benefits over standard pseudospectral and traditional FD methods, but there are many challenges in terms of their performance and parallel implementation, due to RBF-FDs use of relatively large halos and unstructured indexing. With the use of reverse Cuthill-McKee node ordering and tiled transposition of the state variable matrices and RBF-FD differentiation matrices, these challenges were overcome. The RBF-FD solver was implemented for the SWE on the rotating sphere using message passing interface plus OpenMP/OpenACC to demonstrate scalability and performance portability on the three currently dominant high performance computing (HPC) architectures, namely, Intel Xeon multicore, Intel Xeon Phi manycore, and NVIDIA graphics processing unit systems.

关键词： Radial basis function-finite difference radial basis function finite differences shallow water equations reverse Cuthill-McKee message passing interface OpenMP OpenACC scalable algorithms geophysical modeling

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AMIDST: A Java toolbox for scalable probabilistic machine learning

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KNOWLEDGE-BASED SYSTEMS 2019年 163卷 595-597页

作者： Masegosa, Andres R. Martinez, Ana M. Ramos-Lopez, Dario Cabanas, Rafael Salmeron, Antonio Langseth, Helge Nielsen, Thomas D. Madsen, Anders L. Univ Almeria ES-04120 Almeria Spain Aalborg Univ DK-9220 Aalborg Denmark Norwegian Univ Sci & Technol NO-7491 Trondheim Norway HUGIN EXPERT AS DK-9000 Aalborg Denmark Rey Juan Carlos Univ ES-28933 Madrid Spain

The AMIDST Toolbox is an open source Java software for scalable probabilistic machine learning with a special focus on (massive) streaming data. The toolbox supports a flexible modelling language based on probabilistic graphical models with latent variables. AMIDST provides parallel and distributed implementations of scalable algorithms for doing probabilistic inference and Bayesian parameter learning in the specified models. These algorithms are based on a flexible variational message passing scheme, which supports discrete and continuous variables from a wide range of probability distributions. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Probabilistic graphical models scalable algorithms Variational methods Latent variables

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scalable approximations to k-cycle transversal problems on dynamic networks

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KNOWLEDGE AND INFORMATION SYSTEMS 2019年第1期61卷 65-84页

作者： Kuhnle, Alan Crawford, Victoria G. Thai, My T. Univ Florida Comp & Informat Sci & Engn Gainesville FL 32603 USA

We study scalable approximation algorithms for the k-cycle transversal problem, which is to find a minimum-size set of edges that intersects all simple cycles of length k in a network. This problem is relevant to network reliability through the important metric of network clustering coefficient of order k. We formulate two algorithms to be both scalable and have good solution quality in practice: CARL and DARC. DARC is able to efficiently update its solution under dynamic node and edge insertion and removal to the network. In our experimental evaluation, we demonstrate that DARC is able to run on networks with billions of 3-cycles within 2 h and is able to dynamically update its solution in microseconds.

关键词： Dynamic networks Cycle transversal Triangle interdiction scalable algorithms

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scalable TFETI based algorithm with adaptive augmentation for contact problems with variationally consistent discretization of contact conditions

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FINITE ELEMENTS IN ANALYSIS AND DESIGN 2019年 156卷 34-43页

作者： Dostal, Zdenek Vlach, Oldrich Brzobohaty, Tomas VSB Tech Univ Ostrava Fac Elect Engn & Comp Sci Dept Appl Math Ostrava Czech Republic VSB Tech Univ Ostrava Natl Supercomp Ctr IT4Innovat Ostrava Czech Republic

A variationally consistent approximation of contact conditions by means of biorthogonal mortars was introduced by Wohlmuth as a powerful theoretically supported tool for the discretization of contact problems. This approach is especially useful when a potential contact interface is large and curved or when nonmatching grids are applied, but its effective implementation into FETI based algorithms is not straightforward due to the ill conditioning of related inequality constraints. In this paper we review the mortar discretization and theoretical results on scalability of the FETI based algorithm and show that the recently proposed adaptive augmentation can overcome the difficulties caused by the ill-conditioning of constraints. We demonstrate the (weak) numerical scalability by numerical experiments and present the results for a difficult real world problem discretized by mortars that show the power of the new algorithm - the number of iterations required to the solution of this problem discretized by mortars is just one third of that required by the original algorithm for the same problem discretized by node-to-node constraints.

关键词： Contact problems Variationally consistent discretization Mortars scalable algorithms

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Value-added tax fraud detection with scalable anomaly detection techniques

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APPLIED SOFT COMPUTING 2020年 86卷

作者： Vanhoeyveld, Jellis Martens, David Peeters, Bruno Univ Antwerp Fac Appl Econ Prinsstr 13 B-2000 Antwerp Belgium Univ Antwerp Fac Law Venusstr 23 B-2000 Antwerp Belgium

The tax fraud detection domain is characterized by very few labelled data (known fraud/legal cases) that are not representative for the population due to sample selection bias. We use unsupervised anomaly detection (AD) techniques, which are uncommon in tax fraud detection research, to deal with these domain issues. We analyse a unique dataset containing the VAT declarations and client listings of all Belgian VAT numbers pertaining to ten sectors. Our methodology consists in applying AD methods to firms belonging to the same sector and enables an efficient auditing strategy that can be adopted by tax authorities worldwide. The high lifts and hit rates observed in most sectors demonstrate the success of this approach. Sectoral differences exist due to varying market conditions and legal requirements across sectors and we show that the optimal AD method is sector dependent. We focus on three methodological problems that show issues in the related literature. (1) Can we design suitable input features? We develop new fraud indicators from specific fields of the VAT form and client listings and show the predictive value of the combination of these features. (2) Can we design fast algorithms to deal with the large data sizes that can occur in the tax domain? New methods are developed and we demonstrate their scalability both theoretically as well as empirically. (3) How should fraud detection performance be assessed? A new evaluation methodology is proposed that provides reliable performance indications and guarantees that fraud cases are effectively detected by the proposed methods. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Unsupervised anomaly detection Tax fraud detection scalable algorithms

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The Kernel Spatial Scan Statistic 19

The Kernel Spatial Scan Statistic

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27th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems (ACM SIGSPATIAL GIS)

作者： Han, Mingxuan Matheny, Michael Phillips, Jeff M. Univ Utah Salt Lake City UT 84112 USA

ISBN: (纸本)9781450369091

Kulldorff's (1997) seminal paper on spatial scan statistics (SSS) has led to many methods considering different regions of interest, different statistical models, and different approximations while also having numerous applications in epidemiology, environmental monitoring, and homeland security. SSS provides a way to rigorously test for the existence of an anomaly and provide statistical guarantees as to how "anomalous" that anomaly is. However, these methods rely on defining specific regions where the spatial information a point contributes is limited to binary 0 or 1, of either inside or outside the region, while in reality anomalies will tend to follow smooth distributions with decaying density further from an epicenter. In this work, we propose a method that addresses this shortcoming through a continuous scan statistic that generalizes SSS by allowing the point contribution to be defined by a kernel. We provide extensive experimental and theoretical results that shows our methods can be computed efficiently while providing high statistical power for detecting anomalous regions.

关键词： Anomaly detection Spatial Scan Statistics Kernels scalable algorithms

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Accelerated Search for Non-Negative Greedy Sparse Decomposition via Dimensionality Reduction 8

Accelerated Search for Non-Negative Greedy Sparse Decomposit...

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8th Sensor Signal Processing for Defence Conference (SSPD)

作者： Voulgaris, Konstantinos A. Davies, Mike E. Yaghoobi, Mehrdad Univ Edinburgh Inst Digital Commun Edinburgh EH9 3JL Midlothian Scotland

ISBN: (纸本)9781728105031

Non-negative signals form an important class of sparse signals. Many algorithms have already been proposed to recover such non-negative representations, where greedy and convex relaxed algorithms are among the most popular methods. One fast implementation is the FNNOMP algorithm that updates the non-negative coefficients in an iterative manner. Even though FNNOMP is a good approach when working on libraries of small size, the operational time of the algorithm grows significantly when the size of the library is large. This is mainly due to the selection step of the algorithm that relies on matrix vector multiplications. We here introduce the Embedded Nearest Neighbor (E-NN) algorithm which accelerates the search over large datasets while it is guaranteed to find the most correlated atoms. We then replace the selection step of FNNOMP by E-NN. Furthermore we introduce the Update Nearest Neighbor (U-NN) at the look up table of FNNOMP in order to assure the non-negativity criteria of FNNOMP. The results indicate that the proposed methodology can accelerate FNNOMP with a factor 4 on a real dataset of Raman Spectra and with a factor of 22 on a synthetic dataset.

关键词： Matching Pursuit Orthogonal Matching Pursuit Non-negative Sparse Approximations Non-negative Least Square and Spectral Decomposition scalable algorithms Dimensionality Reduction Linear Embedding Raman Spectroscopy

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Global Convection In Earth'S Mantle: Advanced Numerical Methods And Extreme-Scale Simulations

Global Convection In Earth'S Mantle: Advanced Numerical Meth...

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作者： Johann Rudi University of Texas – Austin

学位级别：博士

The thermal convection of rock in Earth's mantle and associated plate tectonics are modeled by nonlinear incompressible Stokes and energy equations. This dissertation focuses on the development of advanced, scalable linear and nonlinear solvers for numerical simulations of realistic instantaneous mantle flow, where we must overcome several computational challenges. The most notable challenges are the severe nonlinearity, heterogeneity, and anisotropy due to the mantle's rheology as well as a wide range of spatial scales and highly localized features. Resolving the crucial small scale features efficiently necessitates adaptive methods, while computational results greatly benefit from a high accuracy per degree of freedom and local mass conservation. Consequently, the discretization of Earth's mantle is carried out by high-order finite elements on aggressively adaptively refined hexahedral meshes with a continuous, nodal velocity approximation and a discontinuous, modal pressure approximation. These velocityÂ â pressure pairings yield optimal asymptotic convergence rates of the finite element approximation to the infinite-dimensional solution with decreasing mesh element size, are inf-sup stable on general, non-conforming hexahedral meshes with "hanging nodes,'' and have the advantage of preserving mass locally at the element level due to the discontinuous pressure. However, because of the difficulties cited above and the desired accuracy, the large implicit systems to be solved are extremely poorly conditioned and sophisticated linear and nonlinear solvers including powerful preconditioning techniques are required. The nonlinear Stokes system is solved using a grid continuation, inexact NewtonÂ â Krylov method. We measure the residual of the momentum equation in the Hâ»Â¹-norm for backtracking line search to avoid overly conservative update steps that are significantly reduced from one. The Newton linearization is augmented by a perturbation of a highly nonlinea

关键词： Partial differential equations Stokes Numerical methods Variable viscosity Schur complement Preconditioning Multigrid scalable algorithms Parallel computing Iterative methods Nonlinear problems Inexact Newton-Krylov methods Mantle convection

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Parallelization and scalability analysis of inverse factorization using the chunks and tasks programming model

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PARALLEL COMPUTING 2019年 89卷 102548-000页

作者： Artemov, Anton G. Rudberg, Elias Rubensson, Emanuel H. Uppsala Univ Dept Informat Technol Div Sci Comp Box 337 SE-75105 Uppsala Sweden

We present three methods for distributed memory parallel inverse factorization of block-sparse Hermitian positive definite matrices. The three methods are a recursive variant of the AINV inverse Cholesky algorithm, iterative refinement, and localized inverse factorization. All three methods are implemented using the Chunks and Tasks programming model, building on the distributed sparse quad-tree matrix representation and parallel matrix-matrix multiplication in the publicly available Chunks and Tasks Matrix Library (CHTML). Although the algorithms are generally applicable, this work was mainly motivated by the need for efficient and scalable inverse factorization of the basis set overlap matrix in large scale electronic structure calculations. We perform various computational tests on overlap matrices for quasi linear glutamic acid-alanine molecules and three-dimensional water clusters discretized using the standard Gaussian basis set STO-3G with up to more than 10 million basis functions. We show that for such matrices the computational cost increases only linearly with system size for all the three methods. We show both theoretically and in numerical experiments that the methods based on iterative refinement and localized inverse factorization outperform previous parallel implementations in weak scaling tests where the system size is increased in direct proportion to the number of processes. We show also that, compared to the method based on pure iterative refinement, the localized inverse factorization requires much less communication. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Parallel computing Sparse matrix algorithms scalable algorithms Large-scale computing Algorithm analysis

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A scalable solution strategy for high-order stabilized finite-element solvers using an implicit line preconditioner

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2018年第Nov.1期341卷 956-984页

作者： Ahrabi, Behzad R. Mavriplis, Dimitri J. Univ Wyoming Dept Mech Engn Laramie WY 82071 USA

This paper presents a robust, efficient, and strongly scalable solution methodology for simulation of complex turbulent flows on unstructured grids. The compressible Reynolds averaged Navier-Stokes (RANS) equations and the negative Spalart-Allmaras (SA) turbulence model are discretized, in coupled form, using a Streamline Upwind Petrov-Galerkin (SUPG) scheme. The time integration is fully implicit, and the discretized equations are advanced towards a steady-state solution using a pseudo-transient continuation (PTC). For solution of the linearized systems, a preconditioned Krylov solver is used. Seeking robustness, Krylov solvers are commonly preconditioned using incomplete factorization methods such as ILU(k). However, these methods are neither memory efficient, nor strongly scalable. To provide a better alternative, the implicit line solution method, which has been traditionally used in finite-volume methods, is revised and enhanced to solve stiffer linear systems. In the developed method, the lines are generated using a matrix-based approach, which connects the strongly-coupled unknowns. In addition, to improve the robustness of the line solver for high-CFL systems, a dual-CFL strategy, with a lower CFL number in the preconditioner matrix, is developed. Also, it is shown that for high-order continuous finite-element discretizations, the interconnections of the degrees of freedom on a line form a banded matrix which is wider than tridiagonal, but still can be factorized completely without generating any fill-ins. The developed line preconditioner is strongly scalable and, in contrast to the ILU factorization, its convergence behavior does not depend on the number of partitions. Two three-dimensional numerical examples are presented in which the performance of the line preconditioner is compared with that of the ILU(k) preconditioner. This comparison shows that, in addition to robustness improvements, the line preconditioner offers significant benefits in terms of m

关键词： Stabilized finite-element methods High-order methods scalable algorithms Implicit line smoothing Turbulent flows Compressible flows

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