arXiv - CS - Mathematical Software最新文献

A prony method variant which surpasses the Adaptive LMS filter in the output signal's representation of input 在输出信号对输入信号的表示方面超越自适应 LMS 滤波器的质子方法变体

arXiv - CS - Mathematical Software Pub Date : 2024-09-02 DOI: arxiv-2409.01272

Parthasarathy Srinivasan

{"title":"A prony method variant which surpasses the Adaptive LMS filter in the output signal's representation of input","authors":"Parthasarathy Srinivasan","doi":"arxiv-2409.01272","DOIUrl":"https://doi.org/arxiv-2409.01272","url":null,"abstract":"The Prony method for approximating signals comprising sinusoidal/exponential\u0000components is known through the pioneering work of Prony in his seminal\u0000dissertation in the year 1795. However, the Prony method saw the light of real\u0000world application only upon the advent of the computational era, which made\u0000feasible the extensive numerical intricacies and labor which the method demands\u0000inherently. The Adaptive LMS Filter which has been the most pervasive method\u0000for signal filtration and approximation since its inception in 1965 does not\u0000provide a consistently assured level of highly precise results as the extended\u0000experiment in this work proves. As a remedy this study improvises upon the\u0000Prony method by observing that a better (more precise) computational\u0000approximation can be obtained under the premise that adjustment can be made for\u0000computational error , in the autoregressive model setup in the initial step of\u0000the Prony computation itself. This adjustment is in proportion to the deviation\u0000of the coefficients in the same autoregressive model. The results obtained by\u0000this improvisation live up to the expectations of obtaining consistency and\u0000higher value in the precision of the output (recovered signal) approximations\u0000as shown in this current work and as compared with the results obtained using\u0000the Adaptive LMS Filter.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"59 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

TorchDA: A Python package for performing data assimilation with deep learning forward and transformation functions TorchDA：利用深度学习前向和转换函数执行数据同化的 Python 软件包

arXiv - CS - Mathematical Software Pub Date : 2024-08-30 DOI: arxiv-2409.00244

Sibo Cheng, Jinyang Min, Che Liu, Rossella Arcucci

{"title":"TorchDA: A Python package for performing data assimilation with deep learning forward and transformation functions","authors":"Sibo Cheng, Jinyang Min, Che Liu, Rossella Arcucci","doi":"arxiv-2409.00244","DOIUrl":"https://doi.org/arxiv-2409.00244","url":null,"abstract":"Data assimilation techniques are often confronted with challenges handling\u0000complex high dimensional physical systems, because high precision simulation in\u0000complex high dimensional physical systems is computationally expensive and the\u0000exact observation functions that can be applied in these systems are difficult\u0000to obtain. It prompts growing interest in integrating deep learning models\u0000within data assimilation workflows, but current software packages for data\u0000assimilation cannot handle deep learning models inside. This study presents a\u0000novel Python package seamlessly combining data assimilation with deep neural\u0000networks to serve as models for state transition and observation functions. The\u0000package, named TorchDA, implements Kalman Filter, Ensemble Kalman Filter\u0000(EnKF), 3D Variational (3DVar), and 4D Variational (4DVar) algorithms, allowing\u0000flexible algorithm selection based on application requirements. Comprehensive\u0000experiments conducted on the Lorenz 63 and a two-dimensional shallow water\u0000system demonstrate significantly enhanced performance over standalone model\u0000predictions without assimilation. The shallow water analysis validates data\u0000assimilation capabilities mapping between different physical quantity spaces in\u0000either full space or reduced order space. Overall, this innovative software\u0000package enables flexible integration of deep learning representations within\u0000data assimilation, conferring a versatile tool to tackle complex high\u0000dimensional dynamical systems across scientific domains.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

HOBOTAN: Efficient Higher Order Binary Optimization Solver with Tensor Networks and PyTorch HOBOTAN：利用张量网络和 PyTorch 的高效高阶二进制优化求解器

arXiv - CS - Mathematical Software Pub Date : 2024-07-29 DOI: arxiv-2407.19987

Shoya Yasuda, Shunsuke Sotobayashi, Yuichiro Minato

引用次数: 0

MPAT: Modular Petri Net Assembly Toolkit MPAT：模块化 Petri 网组装工具包

arXiv - CS - Mathematical Software Pub Date : 2024-07-15 DOI: arxiv-2407.10372

Stefano Chiaradonna, Petar Jevtic, Beckett Sterner

引用次数: 0

Enabling MPI communication within Numba/LLVM JIT-compiled Python code using numba-mpi v1.0 使用 numba-mpi v1.0 在 Numba/LLVM JIT 编译的 Python 代码中启用 MPI 通信

arXiv - CS - Mathematical Software Pub Date : 2024-07-01 DOI: arxiv-2407.13712

Kacper Derlatka, Maciej Manna, Oleksii Bulenok, David Zwicker, Sylwester Arabas

{"title":"Enabling MPI communication within Numba/LLVM JIT-compiled Python code using numba-mpi v1.0","authors":"Kacper Derlatka, Maciej Manna, Oleksii Bulenok, David Zwicker, Sylwester Arabas","doi":"arxiv-2407.13712","DOIUrl":"https://doi.org/arxiv-2407.13712","url":null,"abstract":"The numba-mpi package offers access to the Message Passing Interface (MPI)\u0000routines from Python code that uses the Numba just-in-time (JIT) compiler. As a\u0000result, high-performance and multi-threaded Python code may utilize MPI\u0000communication facilities without leaving the JIT-compiled code blocks, which is\u0000not possible with the mpi4py package, a higher-level Python interface to MPI.\u0000For debugging purposes, numba-mpi retains full functionality of the code even\u0000if the JIT compilation is disabled. The numba-mpi API constitutes a thin\u0000wrapper around the C API of MPI and is built around Numpy arrays including\u0000handling of non-contiguous views over array slices. Project development is\u0000hosted at GitHub leveraging the mpi4py/setup-mpi workflow enabling continuous\u0000integration tests on Linux (MPICH, OpenMPI & Intel MPI), macOS (MPICH &\u0000OpenMPI) and Windows (MS MPI). The paper covers an overview of the package\u0000features, architecture and performance. As of v1.0, the following MPI routines\u0000are exposed and covered by unit tests: size/rank, [i]send/[i]recv,\u0000wait[all|any], test[all|any], allreduce, bcast, barrier, scatter/[all]gather &\u0000wtime. The package is implemented in pure Python and depends on numpy, numba\u0000and mpi4py (the latter used at initialization and as a source of utility\u0000routines only). The performance advantage of using numba-mpi compared to mpi4py\u0000is depicted with a simple example, with entirety of the code included in\u0000listings discussed in the text. Application of numba-mpi for handling domain\u0000decomposition in numerical solvers for partial differential equations is\u0000presented using two external packages that depend on numba-mpi: py-pde and\u0000PyMPDATA-MPI.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141737352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

FVEL: Interactive Formal Verification Environment with Large Language Models via Theorem Proving FVEL：通过定理证明建立大型语言模型的交互式形式化验证环境

arXiv - CS - Mathematical Software Pub Date : 2024-06-20 DOI: arxiv-2406.14408

Xiaohan Lin, Qingxing Cao, Yinya Huang, Haiming Wang, Jianqiao Lu, Zhengying Liu, Linqi Song, Xiaodan Liang

{"title":"FVEL: Interactive Formal Verification Environment with Large Language Models via Theorem Proving","authors":"Xiaohan Lin, Qingxing Cao, Yinya Huang, Haiming Wang, Jianqiao Lu, Zhengying Liu, Linqi Song, Xiaodan Liang","doi":"arxiv-2406.14408","DOIUrl":"https://doi.org/arxiv-2406.14408","url":null,"abstract":"Formal verification (FV) has witnessed growing significance with current\u0000emerging program synthesis by the evolving large language models (LLMs).\u0000However, current formal verification mainly resorts to symbolic verifiers or\u0000hand-craft rules, resulting in limitations for extensive and flexible\u0000verification. On the other hand, formal languages for automated theorem\u0000proving, such as Isabelle, as another line of rigorous verification, are\u0000maintained with comprehensive rules and theorems. In this paper, we propose\u0000FVEL, an interactive Formal Verification Environment with LLMs. Specifically,\u0000FVEL transforms a given code to be verified into Isabelle, and then conducts\u0000verification via neural automated theorem proving with an LLM. The joined\u0000paradigm leverages the rigorous yet abundant formulated and organized rules in\u0000Isabelle and is also convenient for introducing and adjusting cutting-edge\u0000LLMs. To achieve this goal, we extract a large-scale FVELER3. The FVELER\u0000dataset includes code dependencies and verification processes that are\u0000formulated in Isabelle, containing 758 theories, 29,125 lemmas, and 200,646\u0000proof steps in total with in-depth dependencies. We benchmark FVELER in the\u0000FVEL environment by first fine-tuning LLMs with FVELER and then evaluating them\u0000on Code2Inv and SV-COMP. The results show that FVEL with FVELER fine-tuned\u0000Llama3- 8B solves 17.39% (69 -> 81) more problems, and Mistral-7B 12% (75 ->\u000084) more problems in SV-COMP. And the proportion of proof errors is reduced.\u0000Project page: https://fveler.github.io/.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"76 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

OpenCAEPoro: A Parallel Simulation Framework for Multiphase and Multicomponent Porous Media Flows OpenCAEPoro：多相和多组分多孔介质流动的并行模拟框架

arXiv - CS - Mathematical Software Pub Date : 2024-06-16 DOI: arxiv-2406.10862

Shizhe Li, Chen-Song Zhang

引用次数: 0

SySTeC: A Symmetric Sparse Tensor Compiler SySTeC：对称稀疏张量编译器

arXiv - CS - Mathematical Software Pub Date : 2024-06-13 DOI: arxiv-2406.09266

Radha Patel, Willow Ahrens, Saman Amarasinghe

{"title":"SySTeC: A Symmetric Sparse Tensor Compiler","authors":"Radha Patel, Willow Ahrens, Saman Amarasinghe","doi":"arxiv-2406.09266","DOIUrl":"https://doi.org/arxiv-2406.09266","url":null,"abstract":"Symmetric and sparse tensors arise naturally in many domains including linear\u0000algebra, statistics, physics, chemistry, and graph theory. Symmetric tensors\u0000are equal to their transposes, so in the $n$-dimensional case we can save up to\u0000a factor of $n!$ by avoiding redundant operations. Sparse tensors, on the other\u0000hand, are mostly zero, and we can save asymptotically by processing only\u0000nonzeros. Unfortunately, specializing for both symmetry and sparsity at the\u0000same time is uniquely challenging. Optimizing for symmetry requires\u0000consideration of $n!$ transpositions of a triangular kernel, which can be\u0000complex and error prone. Considering multiple transposed iteration orders and\u0000triangular loop bounds also complicates iteration through intricate sparse\u0000tensor formats. Additionally, since each combination of symmetry and sparse\u0000tensor formats requires a specialized implementation, this leads to a\u0000combinatorial number of cases. A compiler is needed, but existing compilers\u0000cannot take advantage of both symmetry and sparsity within the same kernel. In\u0000this paper, we describe the first compiler which can automatically generate\u0000symmetry-aware code for sparse or structured tensor kernels. We introduce a\u0000taxonomy for symmetry in tensor kernels, and show how to target each kind of\u0000symmetry. Our implementation demonstrates significant speedups ranging from\u00001.36x for SSYMV to 30.4x for a 5-dimensional MTTKRP over the non-symmetric\u0000state of the art.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141506256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

PETSc/TAO Developments for Early Exascale Systems 为早期超大规模系统开发 PETSc/TAO

arXiv - CS - Mathematical Software Pub Date : 2024-06-12 DOI: arxiv-2406.08646

Richard Tran Mills, Mark Adams, Satish Balay, Jed Brown, Jacob Faibussowitsch, Toby Isaac, Matthew Knepley, Todd Munson, Hansol Suh, Stefano Zampini, Hong Zhang, Junchao Zhang

{"title":"PETSc/TAO Developments for Early Exascale Systems","authors":"Richard Tran Mills, Mark Adams, Satish Balay, Jed Brown, Jacob Faibussowitsch, Toby Isaac, Matthew Knepley, Todd Munson, Hansol Suh, Stefano Zampini, Hong Zhang, Junchao Zhang","doi":"arxiv-2406.08646","DOIUrl":"https://doi.org/arxiv-2406.08646","url":null,"abstract":"The Portable Extensible Toolkit for Scientific Computation (PETSc) library\u0000provides scalable solvers for nonlinear time-dependent differential and\u0000algebraic equations and for numerical optimization via the Toolkit for Advanced\u0000Optimization (TAO). PETSc is used in dozens of scientific fields and is an\u0000important building block for many simulation codes. During the U.S. Department\u0000of Energy's Exascale Computing Project, the PETSc team has made substantial\u0000efforts to enable efficient utilization of the massive fine-grain parallelism\u0000present within exascale compute nodes and to enable performance portability\u0000across exascale architectures. We recap some of the challenges that designers\u0000of numerical libraries face in such an endeavor, and then discuss the many\u0000developments we have made, which include the addition of new GPU backends,\u0000features supporting efficient on-device matrix assembly, better support for\u0000asynchronicity and GPU kernel concurrency, and new communication\u0000infrastructure. We evaluate the performance of these developments on some\u0000pre-exascale systems as well the early exascale systems Frontier and Aurora,\u0000using compute kernel, communication layer, solver, and mini-application\u0000benchmark studies, and then close with a few observations drawn from our\u0000experiences on the tension between portable performance and other goals of\u0000numerical libraries.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"168 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141506257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An extension of C++ with memory-centric specifications for HPC to reduce memory footprints and streamline MPI development C++ 扩展了以内存为中心的 HPC 规范，以减少内存占用并简化 MPI 开发

arXiv - CS - Mathematical Software Pub Date : 2024-06-10 DOI: arxiv-2406.06095

Pawel K. Radtke, Cristian G. Barrera-Hinojosa, Mladen Ivkovic, Tobias Weinzierl

{"title":"An extension of C++ with memory-centric specifications for HPC to reduce memory footprints and streamline MPI development","authors":"Pawel K. Radtke, Cristian G. Barrera-Hinojosa, Mladen Ivkovic, Tobias Weinzierl","doi":"arxiv-2406.06095","DOIUrl":"https://doi.org/arxiv-2406.06095","url":null,"abstract":"The C++ programming language and its cousins lean towards a\u0000memory-inefficient storage of structs: The compiler inserts helper bits into\u0000the struct such that individual attributes align with bytes, and it adds\u0000additional bytes aligning attributes with cache lines, while it is not able to\u0000exploit knowledge about the range of integers, enums or bitsets to bring the\u0000memory footprint down. Furthermore, the language provides neither support for\u0000data exchange via MPI nor for arbitrary floating-point precision formats. If\u0000developers need to have a low memory footprint and MPI datatypes over structs\u0000which exchange only minimal data, they have to manipulate the data and to write\u0000MPI datatypes manually. We propose a C++ language extension based upon C++\u0000attributes through which developers can guide the compiler what memory\u0000arrangements would be beneficial: Can multiple booleans be squeezed into one\u0000bit field, do floats hold fewer significant bits than in the IEEE standard, or\u0000does the code require a user-defined MPI datatype for certain subsets of\u0000attributes? The extension offers the opportunity to fall back to normal\u0000alignment and padding rules via plain C++ assignments, no dependencies upon\u0000external libraries are introduced, and the resulting code remains standard C++.\u0000Our work implements the language annotations within LLVM and demonstrates their\u0000potential impact, both upon the runtime and the memory footprint, through\u0000smoothed particle hydrodynamics (SPH) benchmarks. They uncover the potential\u0000gains in terms of performance and development productivity.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"233 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141506259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0