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  • Sparse Approximate Multifrontal Factorization with Butterfly Compression for High Frequency Wave Equations
    arXiv.cs.MS Pub Date : 2020-07-01
    Yang Liu; Pieter Ghysels; Lisa Claus; Xiaoye Sherry Li

    We present a fast and approximate multifrontal solver for large-scale sparse linear systems arising from finite-difference, finite-volume or finite-element discretization of high-frequency wave equations. The proposed solver leverages the butterfly algorithm and its hierarchical matrix extension for compressing and factorizing large frontal matrices via graph-distance guided entry evaluation or randomized

    更新日期:2020-07-02
  • Massively parallel 3D computation of the compressible Euler equations with an invariant-domain preserving second-order finite-element scheme
    arXiv.cs.MS Pub Date : 2020-06-30
    Matthias Maier; Martin Kronbichler

    We discuss the efficient implementation of a high-performance second-order colocation-type finite-element scheme for solving the compressible Euler equations of gas dynamics on unstructured meshes. The solver is based on the convex limiting technique introduced by Guermond et al. (SIAM J. Sci. Comput. 40, A3211--A3239, 2018). As such it is invariant-domain preserving, i.e., the solver maintains important

    更新日期:2020-07-02
  • On Designing GPU Algorithms with Applications to Mesh Refinement
    arXiv.cs.MS Pub Date : 2020-07-01
    Zhenghai Chen; Tiow-Seng Tan; Hong-Yang Ong

    We present a set of rules to guide the design of GPU algorithms. These rules are grounded on the principle of reducing waste in GPU utility to achieve good speed up. In accordance to these rules, we propose GPU algorithms for 2D constrained, 3D constrained and 3D Restricted Delaunay refinement problems respectively. Our algorithms take a 2D planar straight line graph (PSLG) or 3D piecewise linear complex

    更新日期:2020-07-02
  • SParSH-AMG: A library for hybrid CPU-GPU algebraic multigrid and preconditioned iterative methods
    arXiv.cs.MS Pub Date : 2020-06-30
    Sashikumaar Ganesan; Manan Shah

    Hybrid CPU-GPU algorithms for Algebraic Multigrid methods (AMG) to efficiently utilize both CPU and GPU resources are presented. In particular, hybrid AMG framework focusing on minimal utilization of GPU memory with performance on par with GPU-only implementations is developed. The hybrid AMG framework can be tuned to operate at a significantly lower GPU-memory, consequently, enables to solve large

    更新日期:2020-07-02
  • Ginkgo: A Modern Linear Operator Algebra Framework for High Performance Computing
    arXiv.cs.MS Pub Date : 2020-06-30
    Hartwig Anzt; Terry Cojean; Goran Flegar; Fritz Goebel; Thomas Gruetzmacher; Pratik Nayak; Tobias Ribizel; Yu-Hsiang Tsai; Enrique S. Quintana-Orti

    In this paper, we present Ginkgo, a modern C++ math library for scientific high performance computing. While classical linear algebra libraries act on matrix and vector objects, Ginkgo's design principle abstracts all functionality as "linear operators", motivating the notation of a "linear operator algebra library". Ginkgo's current focus is oriented towards providing sparse linear algebra functionality

    更新日期:2020-07-01
  • Hierarchical Jacobi Iteration for Structured Matrices on GPUs using Shared Memory
    arXiv.cs.MS Pub Date : 2020-06-30
    Mohammad Shafaet Islam; Qiqi Wang

    High fidelity scientific simulations modeling physical phenomena typically require solving large linear systems of equations which result from discretization of a partial differential equation (PDE) by some numerical method. This step often takes a vast amount of computational time to complete, and therefore presents a bottleneck in simulation work. Solving these linear systems efficiently requires

    更新日期:2020-07-01
  • Adaptive SpMV/SpMSpV on GPUs for Input Vectors of Varied Sparsity
    arXiv.cs.MS Pub Date : 2020-06-30
    Min Li; Yulong Ao; Chao Yang

    Despite numerous efforts for optimizing the performance of Sparse Matrix and Vector Multiplication (SpMV) on modern hardware architectures, few works are done to its sparse counterpart, Sparse Matrix and Sparse Vector Multiplication (SpMSpV), not to mention dealing with input vectors of varied sparsity. The key challenge is that depending on the sparsity levels, distribution of data, and compute platform

    更新日期:2020-07-01
  • The flare Package for High Dimensional Linear Regression and Precision Matrix Estimation in R
    arXiv.cs.MS Pub Date : 2020-06-27
    Xingguo Li; Tuo Zhao; Xiaoming Yuan; Han Liu

    This paper describes an R package named flare, which implements a family of new high dimensional regression methods (LAD Lasso, SQRT Lasso, $\ell_q$ Lasso, and Dantzig selector) and their extensions to sparse precision matrix estimation (TIGER and CLIME). These methods exploit different nonsmooth loss functions to gain modeling flexibility, estimation robustness, and tuning insensitiveness. The developed

    更新日期:2020-06-30
  • Preparing Ginkgo for AMD GPUs -- A Testimonial on Porting CUDA Code to HIP
    arXiv.cs.MS Pub Date : 2020-06-25
    Yuhsiang M. TsaiKarlsruhe Institute of Technology; Terry CojeanKarlsruhe Institute of Technology; Tobias RibizelKarlsruhe Institute of Technology; Hartwig AnztKarlsruhe Institute of TechnologyUniversity of Tennessee, Innovative Computing Lab

    With AMD reinforcing their ambition in the scientific high performance computing ecosystem, we extend the hardware scope of the Ginkgo linear algebra package to feature a HIP backend for AMD GPUs. In this paper, we report and discuss the porting effort from CUDA, the extension of the HIP framework to add missing features such as cooperative groups, the performance price of compiling HIP code for AMD

    更新日期:2020-06-26
  • Index handling and assign optimization for Algorithmic Differentiation reuse index managers
    arXiv.cs.MS Pub Date : 2020-06-23
    Max Sagebaum; Johannes Blühdorn; Nicolas R. Gauger

    For operator overloading Algorithmic Differentiation tools, the identification of primal variables and adjoint variables is usually done via indices. Two common schemes exist for their management and distribution. The linear approach is easy to implement and supports memory optimization with respect to copy statements. On the other hand, the reuse approach requires more implementation effort but results

    更新日期:2020-06-24
  • Robust and scalable h-adaptive aggregated unfitted finite elements for interface elliptic problems
    arXiv.cs.MS Pub Date : 2020-06-19
    Eric Neiva; Santiago Badia

    This work introduces a novel, fully robust and highly-scalable, $h$-adaptive aggregated unfitted finite element method for large-scale interface elliptic problems. The new method is based on a recent distributed-memory implementation of the aggregated finite element method atop a highly-scalable Cartesian forest-of-trees mesh engine. It follows the classical approach of weakly coupling nonmatching

    更新日期:2020-06-22
  • Array Programming with NumPy
    arXiv.cs.MS Pub Date : 2020-06-18
    Charles R. Harris; K. Jarrod Millman; Stéfan J. van der Walt; Ralf Gommers; Pauli Virtanen; David Cournapeau; Eric Wieser; Julian Taylor; Sebastian Berg; Nathaniel J. Smith; Robert Kern; Matti Picus; Stephan Hoyer; Marten H. van Kerkwijk; Matthew Brett; Allan Haldane; Jaime Fernández del Río; Mark Wiebe; Pearu Peterson; Pierre Gérard-Marchant; Kevin Sheppard; Tyler Reddy; Warren Weckesser; Hameer Abbasi;

    Array programming provides a powerful, compact, expressive syntax for accessing, manipulating, and operating on data in vectors, matrices, and higher-dimensional arrays. NumPy is the primary array programming library for the Python language. It plays an essential role in research analysis pipelines in fields as diverse as physics, chemistry, astronomy, geoscience, biology, psychology, material science

    更新日期:2020-06-19
  • Accelerating linear solvers for large-scale Stokes problems with C++ metaprogramming
    arXiv.cs.MS Pub Date : 2020-06-10
    Denis Demidov; Lin Mu; Bin Wang

    Ability to solve large sparse linear systems of equations is very important in modern numerical methods. Creating a solver with a user-friendly interface that can work in many specific scenarios is a challenging task. We describe the C ++ programming techniques that can help in creating flexible and extensible programming interfaces for linear solvers. The approach is based on policy-based design and

    更新日期:2020-06-10
  • On Computing the Kronecker Structure of Polynomial Matrices using Julia
    arXiv.cs.MS Pub Date : 2020-06-09
    Andreas Varga

    In this paper we discuss the mathematical background and the computational aspects which underly the implementation of a collection of Julia functions in the MatrixPencils package for the determination of structural properties of polynomial matrices. We primarily focus on the computation of the finite and infinite spectral structures (e.g., eigenvalues, zeros, poles) as well as the left and right singular

    更新日期:2020-06-09
  • The aggregated unfitted finite element method on parallel tree-based adaptive meshes
    arXiv.cs.MS Pub Date : 2020-06-09
    Santiago Badia; Alberto F. Martín; Eric Neiva; Francesc Verdugo

    In this work, we present an adaptive unfitted finite element scheme that combines the aggregated finite element method with parallel adaptive mesh refinement. We introduce a novel scalable distributed-memory implementation of the resulting scheme on locally-adapted Cartesian forest-of-trees meshes. We propose a two-step algorithm to construct the finite element space at hand that carefully mixes aggregation

    更新日期:2020-06-09
  • AutoMat -- Automatic Differentiation for Generalized Standard Materials on GPUs
    arXiv.cs.MS Pub Date : 2020-06-08
    Johannes Blühdorn; Nicolas R. Gauger; Matthias Kabel

    We propose a universal method for the evaluation of generalized standard materials that greatly simplifies the material law implementation process. By means of automatic differentiation and a numerical integration scheme, AutoMat reduces the implementation effort to two potential functions. By moving AutoMat to the GPU, we close the performance gap to conventional evaluation routines and demonstrate

    更新日期:2020-06-08
  • copent: Estimating Copula Entropy in R
    arXiv.cs.MS Pub Date : 2020-05-27
    Jian Ma

    Statistical independence and conditional independence are the fundemental concepts in statistics and machine learning. Copula Entropy is a mathematical concept for multivariate statistical independence measuring and testing, and also closely related to conditional independence or transfer entropy. It has been applied to solve several statistical or machine learning problems, including association discovery

    更新日期:2020-05-27
  • Model Evidence with Fast Tree Based Quadrature
    arXiv.cs.MS Pub Date : 2020-05-22
    Thomas Foster; Chon Lok Lei; Martin Robinson; David Gavaghan; Ben Lambert

    High dimensional integration is essential to many areas of science, ranging from particle physics to Bayesian inference. Approximating these integrals is hard, due in part to the difficulty of locating and sampling from regions of the integration domain that make significant contributions to the overall integral. Here, we present a new algorithm called Tree Quadrature (TQ) that separates this sampling

    更新日期:2020-05-22
  • SymJAX: symbolic CPU/GPU/TPU programming
    arXiv.cs.MS Pub Date : 2020-05-21
    Randall Balestriero

    SymJAX is a symbolic programming version of JAX simplifying graph input/output/updates and providing additional functionalities for general machine learning and deep learning applications. From an user perspective SymJAX provides a la Theano experience with fast graph optimization/compilation and broad hardware support, along with Lasagne-like deep learning functionalities.

    更新日期:2020-05-21
  • High-Performance GPU and CPU Signal Processing for a Reverse-GPS Wildlife Tracking System
    arXiv.cs.MS Pub Date : 2020-05-21
    Yaniv Rubinpur; Sivan Toledo

    We present robust high-performance implementations of signal-processing tasks performed by a high-throughput wildlife tracking system called ATLAS. The system tracks radio transmitters attached to wild animals by estimating the time of arrival of packets encoding known pseudo-random codes to receivers (base stations). Time-of-arrival estimation of wideband radio signals is computatoinally expensive

    更新日期:2020-05-21
  • Batched computation of the singular value decompositions of order two by the AVX-512 vectorization
    arXiv.cs.MS Pub Date : 2020-05-15
    Vedran Novaković

    In this paper a vectorized algorithm for simultaneously computing up to eight singular value decompositions (SVDs, each of the form $A=U\Sigma V^{\ast}$) of real or complex matrices of order two is proposed. The algorithm extends to a batch of matrices of an arbitrary length $n$, that arises, for example, in the annihilation part of the parallel Kogbetliantz algorithm for the SVD of a square matrix

    更新日期:2020-05-15
  • Reproducibility of Parallel Preconditioned Conjugate Gradient in Hybrid Programming Environments
    arXiv.cs.MS Pub Date : 2020-05-14
    Roman Iakymchuk; Maria Barreda; Stef Graillat; Jose I. Aliaga; Enrique S. Quintana-Orti

    The Preconditioned Conjugate Gradient method is often employed for the solution of linear systems of equations arising in numerical simulations of physical phenomena. While being widely used, the solver is also known for its lack of accuracy while computing the residual. In this article, we propose two algorithmic solutions that originate from the ExBLAS project to enhance the accuracy of the solver

    更新日期:2020-05-14
  • The JuliaConnectoR: a functionally oriented interface for integrating Julia in R
    arXiv.cs.MS Pub Date : 2020-05-13
    Stefan Lenz; Maren Hackenberg; Harald Binder

    Like many groups considering the new programming language Julia, we faced the challenge of accessing the algorithms that we develop in Julia from R. Therefore, we developed the R package JuliaConnectoR, available from the CRAN repository and GitHub (https://github.com/stefan-m-lenz/JuliaConnectoR), in particular for making advanced deep learning tools available. For maintainability and stability, we

    更新日期:2020-05-13
  • SciANN: A Keras wrapper for scientific computations and physics-informed deep learning using artificial neural networks
    arXiv.cs.MS Pub Date : 2020-05-11
    Ehsan Haghighat; Ruben Juanes

    In this paper, we introduce SciANN, a Python package for scientific computing and physics-informed deep learning using artificial neural networks. SciANN uses the widely used deep-learning packages Tensorflow and Keras to build deep neural networks and optimization models, thus inheriting many of Keras's functionalities, such as batch optimization and model reuse for transfer learning. SciANN is designed

    更新日期:2020-05-11
  • A modular extension for a computer algebra system
    arXiv.cs.MS Pub Date : 2020-05-11
    Migran N. Gevorkyan; Anna V. Korolkova; Dmitry S. Kulyabov; Leonid A. Sevastianov

    Computer algebra systems are complex software systems that cover a wide range of scientific and practical problems. However, the absolute coverage cannot be achieved. Often, it is required to create a user extension for an existing computer algebra system. In this case, the extensibility of the system should be taken into account. In this paper, we consider a technology for extending the SymPy computer

    更新日期:2020-05-11
  • AutoHOOT: Automatic High-Order Optimization for Tensors
    arXiv.cs.MS Pub Date : 2020-05-10
    Linjian Ma; Jiayu Ye; Edgar Solomonik

    High-order optimization methods, including Newton's method and its variants as well as alternating minimization methods, dominate the optimization algorithms for tensor decompositions and tensor networks. These tensor methods are used for data analysis and simulation of quantum systems. In this work, we introduce AutoHOOT, the first automatic differentiation (AD) framework targeting at high-order optimization

    更新日期:2020-05-10
  • Delayed approximate matrix assembly in multigrid with dynamic precisions
    arXiv.cs.MS Pub Date : 2020-05-07
    Charles D. Murray; Tobias Weinzierl

    The accurate assembly of the system matrix is an important step in any code that solves partial differential equations on a mesh. We either explicitly set up a matrix, or we work in a matrix-free environment where we have to be able to quickly return matrix entries upon demand. Either way, the construction can become costly due to non-trivial material parameters entering the equations, multigrid codes

    更新日期:2020-05-07
  • Custom-Precision Mathematical Library Explorations for Code Profiling and Optimization
    arXiv.cs.MS Pub Date : 2020-05-06
    David DefourLP2A; Pablo de Oliveira CastroPRISM, LI-PaRAD; Matei IstoanUVSQ, LI-PaRAD; Eric Petit

    The typical processors used for scientific computing have fixed-width data-paths. This implies that mathematical libraries were specifically developed to target each of these fixed precisions (binary16, binary32, binary64). However, to address the increasing energy consumption and throughput requirements of scientific applications, library and hardware designers are moving beyond this one-size-fits-all

    更新日期:2020-05-06
  • CS-TSSOS: Correlative and term sparsity for large-scale polynomial optimization
    arXiv.cs.MS Pub Date : 2020-05-06
    Jie Wang; Victor Magron; Jean B. Lasserre; Ngoc Hoang Anh Mai

    This work proposes a new moment-SOS hierarchy, called CS-TSSOS, for solving large-scale sparse polynomial optimization problems. Its novelty is to exploit simultaneously correlative sparsity and term sparsity by combining advantages of two existing frameworks for sparse polynomial optimization. The former is due to Waki et al. while the latter was initially proposed by Wang et al. and later exploited

    更新日期:2020-05-06
  • Synergistic CPU-FPGA Acceleration of Sparse Linear Algebra
    arXiv.cs.MS Pub Date : 2020-04-29
    Mohammadreza Soltaniyeh; Richard P. Martin; Santosh Nagarakatte

    This paper describes REAP, a software-hardware approach that enables high performance sparse linear algebra computations on a cooperative CPU-FPGA platform. REAP carefully separates the task of organizing the matrix elements from the computation phase. It uses the CPU to provide a first-pass re-organization of the matrix elements, allowing the FPGA to focus on the computation. We introduce a new intermediate

    更新日期:2020-04-29
  • Related by Similiarity: Poristic Triangles and 3-Periodics in the Elliptic Billiard
    arXiv.cs.MS Pub Date : 2020-04-28
    Ronaldo Garcia; Dan Reznik

    Discovered by William Chapple in 1746, the Poristic family is a set of variable-perimeter triangles with common Incircle and Circumcircle. By definition, the family has constant Inradius-to-Circumradius ratio. Interestingly, this invariance also holds for the family of 3-periodics in the Elliptic Billiard, though here Inradius and Circumradius are variable and perimeters are constant. Indeed, we show

    更新日期:2020-04-28
  • Various Ways to Quantify BDMPs
    arXiv.cs.MS Pub Date : 2020-04-28
    Marc BouissouEDF; Shahid KhanRWTH Aachen University; Joost-Pieter KatoenRWTH Aachen University; Pavel KrcalLloyd's Register

    A Boolean logic driven Markov process (BDMP) is a dependability analysis model that defines a continuous-time Markov chain (CTMC). This formalism has high expressive power, yet it remains readable because its graphical representation stays close to standard fault trees. The size of a BDMP is roughly speaking proportional to the size of the system it models, whereas the size of the CTMC specified by

    更新日期:2020-04-28
  • Enhancements to the DIDO Optimal Control Toolbox
    arXiv.cs.MS Pub Date : 2020-04-27
    I. M. Ross

    In 2020, DIDO turned 20! The software package emerged in 2001 as a basic, user-friendly MATLAB teaching-tool to illustrate the various nuances of Pontryagin's Principle but quickly rose to prominence in 2007 after NASA announced it had executed a globally optimal maneuver using DIDO. Since then, the toolbox has grown in applications well beyond its aerospace roots: from solving problems in quantum

    更新日期:2020-04-27
  • GAPS: Generator for Automatic Polynomial Solvers
    arXiv.cs.MS Pub Date : 2020-04-24
    Bo Li; Viktor Larsson

    Minimal problems in computer vision raise the demand of generating efficient automatic solvers for polynomial equation systems. Given a polynomial system repeated with different coefficient instances, the traditional Gr\"obner basis or normal form based solution is very inefficient. Fortunately the Gr\"obner basis of a same polynomial system with different coefficients is found to share consistent

    更新日期:2020-04-24
  • A user-guide to Gridap -- grid-based approximation of partial differential equations in Julia
    arXiv.cs.MS Pub Date : 2019-10-03
    Francesc Verdugo; Santiago Badia

    We present Gridap, a new scientific software library for the numerical approximation of partial differential equations (PDEs) using grid-based approximations. Gridap is an open-source software project exclusively written in the Julia programming language. The main motivation behind the development of this library is to provide an easy-to-use framework for the development of complex PDE solvers in a

    更新日期:2020-04-23
  • GPU Fast Convolution via the Overlap-and-Save Method in Shared Memory
    arXiv.cs.MS Pub Date : 2019-10-04
    Karel Adámek; Sofia Dimoudi; Mike Giles; Wesley Armour

    We present an implementation of the overlap-and-save method, a method for the convolution of very long signals with short response functions, which is tailored to GPUs. We have implemented several FFT algorithms (using the CUDA programming language) which exploit GPU shared memory, allowing for GPU accelerated convolution. We compare our implementation with an implementation of the overlap-and-save

    更新日期:2020-04-13
  • The open-box system: Room and Proctor Intelligent Decider for large scale tests programming RaPID-OMEGA
    arXiv.cs.MS Pub Date : 2019-11-14
    Fernando A. Morales

    We present the mathematical modeling for the problem of choosing rooms and proctoring crews for massive tests, together with its implementation as the open-box system RaPID\Lightning$ \Omega $. The mathematical model is a binary integer programming problem: a combination of the 0-1 Knapsack problem and the job-assignment problem. The model makes decisions according the following criteria in order of

    更新日期:2020-04-13
  • Automatic Differentiation in ROOT
    arXiv.cs.MS Pub Date : 2020-04-09
    Vassil VassilevPrinceton University; Aleksandr EfremovPrinceton University; Oksana ShaduraUniversity of Nebraska Lincoln

    In mathematics and computer algebra, automatic differentiation (AD) is a set of techniques to evaluate the derivative of a function specified by a computer program. AD exploits the fact that every computer program, no matter how complicated, executes a sequence of elementary arithmetic operations (addition, subtraction, multiplication, division, etc.), elementary functions (exp, log, sin, cos, etc

    更新日期:2020-04-10
  • Geomstats: A Python Package for Riemannian Geometry in Machine Learning
    arXiv.cs.MS Pub Date : 2020-04-07
    Nina Miolane; Alice Le Brigant; Johan Mathe; Benjamin Hou; Nicolas Guigui; Yann Thanwerdas; Stefan Heyder; Olivier Peltre; Niklas Koep; Hadi Zaatiti; Hatem Hajri; Yann Cabanes; Thomas Gerald; Paul Chauchat; Christian Shewmake; Bernhard Kainz; Claire Donnat; Susan Holmes; Xavier Pennec

    We introduce Geomstats, an open-source Python toolbox for computations and statistics on nonlinear manifolds, such as hyperbolic spaces, spaces of symmetric positive definite matrices, Lie groups of transformations, and many more. We provide object-oriented and extensively unit-tested implementations. Among others, manifolds come equipped with families of Riemannian metrics, with associated exponential

    更新日期:2020-04-10
  • A generic finite element framework on parallel tree-based adaptive meshes
    arXiv.cs.MS Pub Date : 2019-07-08
    Santiago Badia; Alberto F. Martín; Eric Neiva; Francesc Verdugo

    In this work we formally derive and prove the correctness of the algorithms and data structures in a parallel, distributed-memory, generic finite element framework that supports h-adaptivity on computational domains represented as forest-of-trees. The framework is grounded on a rich representation of the adaptive mesh suitable for generic finite elements that is built on top of a low-level, light-weight

    更新日期:2020-04-10
  • Maintaining a Library of Formal Mathematics
    arXiv.cs.MS Pub Date : 2020-04-07
    Floris van Doorn; Gabriel Ebner; Robert Y. Lewis

    The Lean mathematical library mathlib is developed by a community of users with very different backgrounds and levels of experience. To lower the barrier of entry for contributors and to lessen the burden of reviewing contributions, we have developed a number of tools for the library which check proof developments for subtle mistakes in the code and generate documentation suited for our varied audience

    更新日期:2020-04-09
  • The DUNE Framework: Basic Concepts and Recent Developments
    arXiv.cs.MS Pub Date : 2019-09-30
    Peter Bastian; Markus Blatt; Andreas Dedner; Nils-Arne Dreier; Christian Engwer; René Fritze; Carsten Gräser; Christoph Grüninger; Dominic Kempf; Robert Klöfkorn; Mario Ohlberger; Oliver Sander

    This paper presents the basic concepts and the module structure of the Distributed and Unified Numerics Environment and reflects on recent developments and general changes that happened since the release of the first Dune version in 2007 and the main papers describing that state [1, 2]. This discussion is accompanied with a description of various advanced features, such as coupling of domains and cut

    更新日期:2020-04-08
  • Interpolation of Dense and Sparse Rational Functions and other Improvements in $\texttt{FireFly}$
    arXiv.cs.MS Pub Date : 2020-04-03
    Jonas Klappert; Sven Yannick Klein; Fabian Lange

    We present the main improvements and new features in version $\texttt{2.0}$ of the open-source $\texttt{C++}$ library $\texttt{FireFly}$ for the interpolation of rational functions. This includes algorithmic improvements, e.g. a hybrid algorithm for dense and sparse rational functions and an algorithm to identify and remove univariate factors. The new version is applied to a Feynman-integral reduction

    更新日期:2020-04-06
  • Surrogate-assisted performance tuning of knowledge discovery algorithms: application to clinical pathway evolutionary modeling
    arXiv.cs.MS Pub Date : 2020-04-02
    Anastasia A. Funkner; Aleksey N. Yakovlev; Sergey V. Kovalchuk

    The paper proposes an approach for surrogate-assisted tuning of knowledge discovery algorithms. The approach is based on the prediction of both the quality and performance of the target algorithm. The prediction is furtherly used as objectives for the optimization and tuning of the algorithm. The approach is investigated using clinical pathways (CP) discovery problem resolved using the evolutionary-based

    更新日期:2020-04-03
  • Vectorization and Minimization of Memory Footprint for Linear High-Order Discontinuous Galerkin Schemes
    arXiv.cs.MS Pub Date : 2020-03-28
    Jean-Matthieu Gallard; Leonhard Rannabauer; Anne Reinarz; Michael Bader

    We present a sequence of optimizations to the performance-critical compute kernels of the high-order discontinuous Galerkin solver of the hyperbolic PDE engine ExaHyPE -- successively tackling bottlenecks due to SIMD operations, cache hierarchies and restrictions in the software design. Starting from a generic scalar implementation of the numerical scheme, our first optimized variant applies state-of-the-art

    更新日期:2020-03-31
  • Making RooFit Ready for Run 3
    arXiv.cs.MS Pub Date : 2020-03-28
    Stephan Hageboeck; Lorenzo Moneta

    RooFit and RooStats, the toolkits for statistical modelling in ROOT, are used in most searches and measurements at the Large Hadron Collider. The data to be collected in Run 3 will enable measurements with higher precision and models with larger complexity, but also require faster data processing. In this work, first results on modernising RooFit's collections, restructuring data flow and vectorising

    更新日期:2020-03-31
  • A Faster, More Intuitive RooFit
    arXiv.cs.MS Pub Date : 2020-03-28
    Stephan Hageboeck

    RooFit and RooStats, the toolkits for statistical modelling in ROOT, are used in most searches and measurements at the Large Hadron Collider as well as at $B$ factories. Larger datasets to be collected in e.g. the LHC's Run 3 will enable measurements with higher precision, but will require faster data processing to keep fitting times stable. In this work, a simplification of RooFit's interfaces and

    更新日期:2020-03-31
  • Role-Oriented Code Generation in an Engine for Solving Hyperbolic PDE Systems
    arXiv.cs.MS Pub Date : 2019-11-15
    Jean-Matthieu Gallard; Lukas Krenz; Leonhard Rannabauer; Anne Reinarz; Michael Bader

    The development of a high performance PDE solver requires the combined expertise of interdisciplinary teams with respect to application domain, numerical scheme and low-level optimization. In this paper, we present how the ExaHyPE engine facilitates the collaboration of such teams by isolating three roles: application, algorithms, and optimization expert. We thus support team members in letting them

    更新日期:2020-03-31
  • Geometric Sparsification of Closeness Relations: Eigenvalue Clustering for Computing Matrix Functions
    arXiv.cs.MS Pub Date : 2020-03-23
    Nir Goren; Dan Halperin; Sivan Toledo

    We show how to efficiently solve a clustering problem that arises in a method to evaluate functions of matrices. The problem requires finding the connected components of a graph whose vertices are eigenvalues of a real or complex matrix and whose edges are pairs of eigenvalues that are at most \delta away from each other. Davies and Higham proposed solving this problem by enumerating the edges of the

    更新日期:2020-03-28
  • FlexRiLoG -- A SageMath Package for Motions of Graphs
    arXiv.cs.MS Pub Date : 2020-03-26
    Georg Grasegger; Jan Legerský

    In this paper we present the SageMath package FlexRiLoG (short for flexible and rigid labelings of graphs). Based on recent results the software generates motions of graphs using special edge colorings. The package computes and illustrates the colorings and the motions. We present the structure and usage of the package.

    更新日期:2020-03-28
  • bertha: Project Skeleton for Scientific Software
    arXiv.cs.MS Pub Date : 2019-12-03
    Michael Riesch; Tien Dat Nguyen; Christian Jirauschek

    Science depends heavily on reliable and easy-to-use software packages, such as mathematical libraries or data analysis tools. Developing such packages requires a lot of effort, which is too often avoided due to the lack of funding or recognition. In order to reduce the efforts required to create sustainable software packages, we present a project skeleton that ensures the best software engineering

    更新日期:2020-03-28
  • Scalable parallel algorithm for solving non-stationary systems of linear inequalities
    arXiv.cs.MS Pub Date : 2020-03-22
    Leonid B. Sokolinsky; Irina M. Sokolinskaya

    In this paper, a scalable iterative projection-type algorithm for solving non-stationary sys-tems of linear inequalities is considered. A non-stationary system is understood as a large-scale system of inequalities in which coefficients and constant terms can change during the calculation process. The proposed parallel algorithm uses the concept of pseudo-projection which generalizes the notion of orthogonal

    更新日期:2020-03-24
  • Semi-Lagrangian Vlasov simulation on GPUs
    arXiv.cs.MS Pub Date : 2019-07-18
    Lukas Einkemmer

    In this paper, our goal is to efficiently solve the Vlasov equation on GPUs. A semi-Lagrangian discontinuous Galerkin scheme is used for the discretization. Such kinetic computations are extremely expensive due to the high-dimensional phase space. The SLDG code, which is publicly available under the MIT license abstracts the number of dimensions and uses a shared codebase for both GPU and CPU based

    更新日期:2020-03-18
  • Pressio: Enabling projection-based model reduction for large-scale nonlinear dynamical systems
    arXiv.cs.MS Pub Date : 2020-03-17
    Francesco Rizzi; Patrick J. Blonigan; Kevin T. Carlberg

    This work introduces Pressio, an open-source project aimed at enabling leading-edge projection-based reduced order models (ROMs) for large-scale nonlinear dynamical systems in science and engineering. Pressio provides model-reduction methods that can reduce both the number of spatial and temporal degrees of freedom for any dynamical system expressible as a system of parameterized ordinary differential

    更新日期:2020-03-17
  • FunGrim: a symbolic library for special functions
    arXiv.cs.MS Pub Date : 2020-03-13
    Fredrik JohanssonLFANT

    We present the Mathematical Functions Grimoire (FunGrim), a website and database of formulas and theorems for special functions. We also discuss the symbolic computation library used as the backend and main development tool for FunGrim, and the Grim formula language used in these projects to represent mathematical content semantically.

    更新日期:2020-03-16
  • An R Package for generating covariance matrices for maximum-entropy sampling from precipitation chemistry data
    arXiv.cs.MS Pub Date : 2020-03-13
    Hessa Al-Thani; Jon Lee

    We present an open-source R package (MESgenCov v 0.1.0) for temporally fitting multivariate precipitation chemistry data and extracting a covariance matrix for use in the MESP (maximum-entropy sampling problem). We provide multiple functionalities for modeling and model assessment. The package is tightly coupled with NADP/NTN (National Atmospheric Deposition Program / National Trends Network) data

    更新日期:2020-03-16
  • Evaluating Abstract Asynchronous Schwarz solvers on GPUs
    arXiv.cs.MS Pub Date : 2020-03-11
    Pratik Nayak; Terry Cojean; Hartwig Anzt

    With the commencement of the exascale computing era, we realize that the majority of the leadership supercomputers are heterogeneous and massively parallel even on a single node with multiple co-processors such as GPUs and multiple cores on each node. For example, ORNLs Summit accumulates six NVIDIA Tesla V100s and 42 core IBM Power9s on each node. Synchronizing across all these compute resources in

    更新日期:2020-03-11
  • AirCROP: Airline Crew Pairing Optimizer for Complex Flight Networks Involving Multiple Crew Bases & Billion-Plus Variables
    arXiv.cs.MS Pub Date : 2020-03-09
    Divyam Aggarwal; Dhish Kumar Saxena; Thomas Bäck; Michael Emmerich

    Airline scheduling poses some of the most challenging problems in the entire Operations Research (OR) domain. In that, crew scheduling (CS) constitutes one of the most important and challenging planning activities. Notably, the crew operating cost is the second-largest component of an airline's total operating cost (after the fuel cost). Hence, its optimization promises enormous benefits, and even

    更新日期:2020-03-10
  • Flexible numerical optimization with ensmallen
    arXiv.cs.MS Pub Date : 2020-03-09
    Ryan R. Curtin; Marcus Edel; Rahul Ganesh Prabhu; Suryoday Basak; Zhihao Lou; Conrad Sanderson

    This report provides an introduction to the ensmallen numerical optimization library, as well as a deep dive into the technical details of how it works. The library provides a fast and flexible C++ framework for mathematical optimization of arbitrary user-supplied functions. A large set of pre-built optimizers is provided, including many variants of Stochastic Gradient Descent and Quasi-Newton optimizers

    更新日期:2020-03-10
  • COMPLEX-IT: A Case-Based Modeling and Scenario Simulation Platform for Social Inquiry
    arXiv.cs.MS Pub Date : 2020-03-06
    Corey Schimpf; Brian Castellani

    COMPLEX-IT is a case-based, mixed-methods platform for social inquiry into complex data/systems, designed to increase non-expert access to the tools of computational social science (i.e., cluster analysis, artificial intelligence, data visualization, data forecasting, and scenario simulation). In particular, COMPLEX-IT aids social inquiry though a heavy emphasis on learning about the complex data/system

    更新日期:2020-03-09
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