Jonathan Julián Huerta y Munive, Simon Foster, Mario Gleirscher, Georg Struth, Christian Pardillo Laursen, Thomas Hickman
We formally introduce IsaVODEs (Isabelle verification with Ordinary Differential Equations), a framework for the verification of cyber-physical systems. We describe the semantic foundations of the framework's formalisation in the Isabelle/HOL proof assistant. A user-friendly language specification based on a robust state model makes our framework flexible and adaptable to various engineering workflows. New additions to the framework increase both its expressivity and proof automation. Specifically, formalisations related to forward diamond correctness specifications, certification of unique solutions to ordinary differential equations (ODEs) as flows, and invariant reasoning for systems of ODEs contribute to the framework's scalability and usability. Various examples and an evaluation validate the effectiveness of our framework.
{"title":"Scalable Automated Verification for Cyber-Physical Systems in Isabelle/HOL","authors":"Jonathan Julián Huerta y Munive, Simon Foster, Mario Gleirscher, Georg Struth, Christian Pardillo Laursen, Thomas Hickman","doi":"arxiv-2401.12061","DOIUrl":"https://doi.org/arxiv-2401.12061","url":null,"abstract":"We formally introduce IsaVODEs (Isabelle verification with Ordinary\u0000Differential Equations), a framework for the verification of cyber-physical\u0000systems. We describe the semantic foundations of the framework's formalisation\u0000in the Isabelle/HOL proof assistant. A user-friendly language specification\u0000based on a robust state model makes our framework flexible and adaptable to\u0000various engineering workflows. New additions to the framework increase both its\u0000expressivity and proof automation. Specifically, formalisations related to\u0000forward diamond correctness specifications, certification of unique solutions\u0000to ordinary differential equations (ODEs) as flows, and invariant reasoning for\u0000systems of ODEs contribute to the framework's scalability and usability.\u0000Various examples and an evaluation validate the effectiveness of our framework.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139559497","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}
Salwa Tabet GonzalezUniversity of Strasbourg, Predrag JaničićUniversity of Belgrade, Julien NarbouxUniversity of Strasbourg
Conjecturing and theorem proving are activities at the center of mathematical practice and are difficult to separate. In this paper, we propose a framework for completing incomplete conjectures and incomplete proofs. The framework can turn a conjecture with missing assumptions and with an under-specified goal into a proper theorem. Also, the proposed framework can help in completing a proof sketch into a human-readable and machine-checkable proof. Our approach is focused on synthetic geometry, and uses coherent logic and constraint solving. The proposed approach is uniform for all three kinds of tasks, flexible and, to our knowledge, unique such approach.
{"title":"Automated Completion of Statements and Proofs in Synthetic Geometry: an Approach based on Constraint Solving","authors":"Salwa Tabet GonzalezUniversity of Strasbourg, Predrag JaničićUniversity of Belgrade, Julien NarbouxUniversity of Strasbourg","doi":"arxiv-2401.11898","DOIUrl":"https://doi.org/arxiv-2401.11898","url":null,"abstract":"Conjecturing and theorem proving are activities at the center of mathematical\u0000practice and are difficult to separate. In this paper, we propose a framework\u0000for completing incomplete conjectures and incomplete proofs. The framework can\u0000turn a conjecture with missing assumptions and with an under-specified goal\u0000into a proper theorem. Also, the proposed framework can help in completing a\u0000proof sketch into a human-readable and machine-checkable proof. Our approach is\u0000focused on synthetic geometry, and uses coherent logic and constraint solving.\u0000The proposed approach is uniform for all three kinds of tasks, flexible and, to\u0000our knowledge, unique such approach.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139555685","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}
Datasets encountered in scientific and engineering applications appear in complex formats (e.g., images, multivariate time series, molecules, video, text strings, networks). Graph theory provides a unifying framework to model such datasets and enables the use of powerful tools that can help analyze, visualize, and extract value from data. In this work, we present PlasmoData.jl, an open-source, Julia framework that uses concepts of graph theory to facilitate the modeling and analysis of complex datasets. The core of our framework is a general data modeling abstraction, which we call a DataGraph. We show how the abstraction and software implementation can be used to represent diverse data objects as graphs and to enable the use of tools from topology, graph theory, and machine learning (e.g., graph neural networks) to conduct a variety of tasks. We illustrate the versatility of the framework by using real datasets: i) an image classification problem using topological data analysis to extract features from the graph model to train machine learning models; ii) a disease outbreak problem where we model multivariate time series as graphs to detect abnormal events; and iii) a technology pathway analysis problem where we highlight how we can use graphs to navigate connectivity. Our discussion also highlights how PlasmoData.jl leverages native Julia capabilities to enable compact syntax, scalable computations, and interfaces with diverse packages.
科学和工程应用中遇到的数据集格式复杂（如图像、多变量时间序列、分子、视频、文本串、网络）。图论为此类数据集的建模提供了一个统一的框架，使人们能够使用强大的工具来帮助分析、可视化数据并从中提取价值。在这项工作中，我们介绍了 PlasmoData.jl，这是一个开源的 Julia 框架，它使用图论的概念来促进复杂数据集的建模和分析。我们框架的核心是一个通用的数据建模抽象，我们称之为数据图（DataGraph）。我们展示了如何利用该抽象和软件实现将各种数据对象表示为图，并利用拓扑学、图论和机器学习（如图神经网络）工具来完成各种任务。我们通过使用真实数据集来说明该框架的多功能性：i) 图像分类问题，使用拓扑数据分析从图模型中提取特征来训练机器学习模型；ii) 疾病爆发问题，我们将多变量时间序列建模为图来检测异常事件；iii) 技术路径分析问题，我们强调了如何使用图来导航连接性。我们的讨论还强调了 PlasmoData.jl 如何利用原生的 Julia 功能来实现紧凑的语法、可扩展的计算以及与不同软件包的接口。
{"title":"PlasmoData.jl -- A Julia Framework for Modeling and Analyzing Complex Data as Graphs","authors":"David L Cole, Victor M Zavala","doi":"arxiv-2401.11404","DOIUrl":"https://doi.org/arxiv-2401.11404","url":null,"abstract":"Datasets encountered in scientific and engineering applications appear in\u0000complex formats (e.g., images, multivariate time series, molecules, video, text\u0000strings, networks). Graph theory provides a unifying framework to model such\u0000datasets and enables the use of powerful tools that can help analyze,\u0000visualize, and extract value from data. In this work, we present PlasmoData.jl,\u0000an open-source, Julia framework that uses concepts of graph theory to\u0000facilitate the modeling and analysis of complex datasets. The core of our\u0000framework is a general data modeling abstraction, which we call a DataGraph. We\u0000show how the abstraction and software implementation can be used to represent\u0000diverse data objects as graphs and to enable the use of tools from topology,\u0000graph theory, and machine learning (e.g., graph neural networks) to conduct a\u0000variety of tasks. We illustrate the versatility of the framework by using real\u0000datasets: i) an image classification problem using topological data analysis to\u0000extract features from the graph model to train machine learning models; ii) a\u0000disease outbreak problem where we model multivariate time series as graphs to\u0000detect abnormal events; and iii) a technology pathway analysis problem where we\u0000highlight how we can use graphs to navigate connectivity. Our discussion also\u0000highlights how PlasmoData.jl leverages native Julia capabilities to enable\u0000compact syntax, scalable computations, and interfaces with diverse packages.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139559796","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}
Pedro QuaresmaUniversity of Coimbra, Portugal, Zoltán KovácsThe Private University College of Education of the Diocese of Linz, Austria
ADG is a forum to exchange ideas and views, to present research results and progress, and to demonstrate software tools at the intersection between geometry and automated deduction. The conference is held every two years. The previous editions of ADG were held in Hagenberg in 2021 (online, postponed from 2020 due to COVID-19), Nanning in 2018, Strasbourg in 2016, Coimbra in 2014, Edinburgh in 2012, Munich in 2010, Shanghai in 2008, Pontevedra in 2006, Gainesville in 2004, Hagenberg in 2002, Zurich in 2000, Beijing in 1998, and Toulouse in 1996. The 14th edition, ADG 2023, was held in Belgrade, Serbia, in September 20-22, 2023. This edition of ADG had an additional special focus topic, Deduction in Education. Invited Speakers: Julien Narboux, University of Strasbourg, France "Formalisation, arithmetization and automatisation of geometry"; Filip Mari'c, University of Belgrade, Serbia, "Automatization, formalization and visualization of hyperbolic geometry"; Zlatan Magajna, University of Ljubljana, Slovenia, "Workshop OK Geometry"
{"title":"Proceedings 14th International Conference on Automated Deduction in Geometry","authors":"Pedro QuaresmaUniversity of Coimbra, Portugal, Zoltán KovácsThe Private University College of Education of the Diocese of Linz, Austria","doi":"arxiv-2401.10725","DOIUrl":"https://doi.org/arxiv-2401.10725","url":null,"abstract":"ADG is a forum to exchange ideas and views, to present research results and\u0000progress, and to demonstrate software tools at the intersection between\u0000geometry and automated deduction. The conference is held every two years. The\u0000previous editions of ADG were held in Hagenberg in 2021 (online, postponed from\u00002020 due to COVID-19), Nanning in 2018, Strasbourg in 2016, Coimbra in 2014,\u0000Edinburgh in 2012, Munich in 2010, Shanghai in 2008, Pontevedra in 2006,\u0000Gainesville in 2004, Hagenberg in 2002, Zurich in 2000, Beijing in 1998, and\u0000Toulouse in 1996. The 14th edition, ADG 2023, was held in Belgrade, Serbia, in September 20-22,\u00002023. This edition of ADG had an additional special focus topic, Deduction in\u0000Education. Invited Speakers: Julien Narboux, University of Strasbourg, France\u0000\"Formalisation, arithmetization and automatisation of geometry\"; Filip Mari'c,\u0000University of Belgrade, Serbia, \"Automatization, formalization and\u0000visualization of hyperbolic geometry\"; Zlatan Magajna, University of Ljubljana,\u0000Slovenia, \"Workshop OK Geometry\"","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139515030","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}
David A. Ham, Vaclav Hapla, Matthew G. Knepley, Lawrence Mitchell, Koki Sagiyama
In this work, we introduce a new algorithm for N-to-M checkpointing in finite element simulations. This new algorithm allows efficient saving/loading of functions representing physical quantities associated with the mesh representing the physical domain. Specifically, the algorithm allows for using different numbers of parallel processes for saving and loading, allowing for restarting and post-processing on the process count appropriate to the given phase of the simulation and other conditions. For demonstration, we implemented this algorithm in PETSc, the Portable, Extensible Toolkit for Scientific Computation, and added a convenient high-level interface into Firedrake, a system for solving partial differential equations using finite element methods. We evaluated our new implementation by saving and loading data involving 8.2 billion finite element degrees of freedom using 8,192 parallel processes on ARCHER2, the UK National Supercomputing Service.
在这项工作中，我们为有限元模拟中的 N 对 M 检查点引入了一种新算法。这种新算法可以高效地保存/加载与物理域网格相关的物理量函数。具体来说，该算法允许使用不同数量的并行进程进行保存和加载，允许在与给定模拟阶段和其他条件相适应的进程数量上启动和后处理。为了进行演示，我们在 PETSc（用于科学计算的便携式可扩展工具包）中实现了这一算法，并在 Firedrake（使用有限元方法求解偏微分方程的系统）中添加了一个方便的高级接口。我们在英国国家超级计算服务机构ARCHER2 上使用 8192 个并行进程保存和加载了涉及 82 亿个有限元自由度的数据，对我们的新实现进行了评估。
{"title":"Efficient N-to-M Checkpointing Algorithm for Finite Element Simulations","authors":"David A. Ham, Vaclav Hapla, Matthew G. Knepley, Lawrence Mitchell, Koki Sagiyama","doi":"arxiv-2401.05868","DOIUrl":"https://doi.org/arxiv-2401.05868","url":null,"abstract":"In this work, we introduce a new algorithm for N-to-M checkpointing in finite\u0000element simulations. This new algorithm allows efficient saving/loading of\u0000functions representing physical quantities associated with the mesh\u0000representing the physical domain. Specifically, the algorithm allows for using\u0000different numbers of parallel processes for saving and loading, allowing for\u0000restarting and post-processing on the process count appropriate to the given\u0000phase of the simulation and other conditions. For demonstration, we implemented\u0000this algorithm in PETSc, the Portable, Extensible Toolkit for Scientific\u0000Computation, and added a convenient high-level interface into Firedrake, a\u0000system for solving partial differential equations using finite element methods.\u0000We evaluated our new implementation by saving and loading data involving 8.2\u0000billion finite element degrees of freedom using 8,192 parallel processes on\u0000ARCHER2, the UK National Supercomputing Service.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139464659","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}
Hypergraphs, or generalization of graphs such that edges can contain more than two nodes, have become increasingly prominent in understanding complex network analysis. Unlike graphs, hypergraphs have relatively few supporting platforms, and such dearth presents a barrier to more widespread adaptation of hypergraph computational toolboxes that could enable further research in several areas. Here, we introduce HyperRD, a Python package for hypergraph computation, simulation, and interoperability with other powerful Python packages in graph and hypergraph research. Then, we will introduce two models on hypergraph, the general Schelling's model and the SIR model, and simulate them with HyperRD.
超图，即边缘可以包含两个以上节点的图的广义化，在理解复杂网络分析方面日益突出。与图不同，超图的支持平台相对较少，这种匮乏阻碍了超图计算工具箱的广泛应用，而这些工具箱可以促进多个领域的进一步研究。在这里，我们将介绍 HyperRD，这是一个用于超图计算、仿真以及与图和超图研究领域其他强大 Python 软件包互操作的 Python 软件包。然后，我们将介绍两种超图模型：一般谢林模型和 SIR 模型，并用 HyperRD 对它们进行仿真。
{"title":"Toward a comprehensive simulation framework for hypergraphs: a Python-base approach","authors":"Quoc Chuong Nguyen, Trung Kien Le","doi":"arxiv-2401.03917","DOIUrl":"https://doi.org/arxiv-2401.03917","url":null,"abstract":"Hypergraphs, or generalization of graphs such that edges can contain more\u0000than two nodes, have become increasingly prominent in understanding complex\u0000network analysis. Unlike graphs, hypergraphs have relatively few supporting\u0000platforms, and such dearth presents a barrier to more widespread adaptation of\u0000hypergraph computational toolboxes that could enable further research in\u0000several areas. Here, we introduce HyperRD, a Python package for hypergraph\u0000computation, simulation, and interoperability with other powerful Python\u0000packages in graph and hypergraph research. Then, we will introduce two models\u0000on hypergraph, the general Schelling's model and the SIR model, and simulate\u0000them with HyperRD.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139410253","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}
Kai-Hsin Wu, Chang-Teng Lin, Ke Hsu, Hao-Ti Hung, Manuel Schneider, Chia-Min Chung, Ying-Jer Kao, Pochung Chen
We introduce a tensor network library designed for classical and quantum physics simulations called Cytnx (pronounced as sci-tens). This library provides almost an identical interface and syntax for both C++ and Python, allowing users to effortlessly switch between two languages. Aiming at a quick learning process for new users of tensor network algorithms, the interfaces resemble the popular Python scientific libraries like NumPy, Scipy, and PyTorch. Not only multiple global Abelian symmetries can be easily defined and implemented, Cytnx also provides a new tool called Network that allows users to store large tensor networks and perform tensor network contractions in an optimal order automatically. With the integration of cuQuantum, tensor calculations can also be executed efficiently on GPUs. We present benchmark results for tensor operations on both devices, CPU and GPU. We also discuss features and higher-level interfaces to be added in the future.
{"title":"The Cytnx Library for Tensor Networks","authors":"Kai-Hsin Wu, Chang-Teng Lin, Ke Hsu, Hao-Ti Hung, Manuel Schneider, Chia-Min Chung, Ying-Jer Kao, Pochung Chen","doi":"arxiv-2401.01921","DOIUrl":"https://doi.org/arxiv-2401.01921","url":null,"abstract":"We introduce a tensor network library designed for classical and quantum\u0000physics simulations called Cytnx (pronounced as sci-tens). This library\u0000provides almost an identical interface and syntax for both C++ and Python,\u0000allowing users to effortlessly switch between two languages. Aiming at a quick\u0000learning process for new users of tensor network algorithms, the interfaces\u0000resemble the popular Python scientific libraries like NumPy, Scipy, and\u0000PyTorch. Not only multiple global Abelian symmetries can be easily defined and\u0000implemented, Cytnx also provides a new tool called Network that allows users to\u0000store large tensor networks and perform tensor network contractions in an\u0000optimal order automatically. With the integration of cuQuantum, tensor\u0000calculations can also be executed efficiently on GPUs. We present benchmark\u0000results for tensor operations on both devices, CPU and GPU. We also discuss\u0000features and higher-level interfaces to be added in the future.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139102468","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}
In order to fully harness the potential of machine learning, it is crucial to establish a system that renders the field more accessible and less daunting for individuals who may not possess a comprehensive understanding of its intricacies. The paper describes the design of a system that integrates AutoML, XAI, and synthetic data generation to provide a great UX design for users. The system allows users to navigate and harness the power of machine learning while abstracting its complexities and providing high usability. The paper proposes two novel classifiers, Logistic Regression Forest and Support Vector Tree, for enhanced model performance, achieving 96% accuracy on a diabetes dataset and 93% on a survey dataset. The paper also introduces a model-dependent local interpreter called MEDLEY and evaluates its interpretation against LIME, Greedy, and Parzen. Additionally, the paper introduces LLM-based synthetic data generation, library-based data generation, and enhancing the original dataset with GAN. The findings on synthetic data suggest that enhancing the original dataset with GAN is the most reliable way to generate synthetic data, as evidenced by KS tests, standard deviation, and feature importance. The authors also found that GAN works best for quantitative datasets.
为了充分利用机器学习的潜力，必须建立一个系统，让那些对机器学习的复杂性缺乏全面了解的人能够更容易地进入这一领域，而不是望而生畏。本文介绍了一个系统的设计，该系统集成了 AutoML、XAI 和合成数据生成功能，为用户提供了出色的用户体验设计。该系统允许用户浏览和利用机器学习的强大功能，同时抽象其复杂性并提供高可用性。论文提出了两个新颖的分类器--逻辑回归森林和支持向量树，它们提高了模型的性能，在糖尿病数据集上达到了96%的准确率，在调查数据集上达到了93%的准确率。论文还介绍了一种名为 MEDLEY 的依赖模型的本地解释器，并对其与 LIME、Greedy 和 Parzen 的解释效果进行了评估。此外，论文还介绍了基于 LLM 的合成数据生成、基于库的数据生成以及用 GAN 增强原始数据集。对合成数据的研究结果表明，用 GAN 增强原始数据集是生成合成数据最可靠的方法，KS 检验、标准偏差和特征重要性都证明了这一点。作者还发现，GAN 最适用于定量数据集。
{"title":"KAXAI: An Integrated Environment for Knowledge Analysis and Explainable AI","authors":"Saikat Barua, Dr. Sifat Momen","doi":"arxiv-2401.00193","DOIUrl":"https://doi.org/arxiv-2401.00193","url":null,"abstract":"In order to fully harness the potential of machine learning, it is crucial to\u0000establish a system that renders the field more accessible and less daunting for\u0000individuals who may not possess a comprehensive understanding of its\u0000intricacies. The paper describes the design of a system that integrates AutoML,\u0000XAI, and synthetic data generation to provide a great UX design for users. The\u0000system allows users to navigate and harness the power of machine learning while\u0000abstracting its complexities and providing high usability. The paper proposes\u0000two novel classifiers, Logistic Regression Forest and Support Vector Tree, for\u0000enhanced model performance, achieving 96% accuracy on a diabetes dataset and\u000093% on a survey dataset. The paper also introduces a model-dependent local\u0000interpreter called MEDLEY and evaluates its interpretation against LIME,\u0000Greedy, and Parzen. Additionally, the paper introduces LLM-based synthetic data\u0000generation, library-based data generation, and enhancing the original dataset\u0000with GAN. The findings on synthetic data suggest that enhancing the original\u0000dataset with GAN is the most reliable way to generate synthetic data, as\u0000evidenced by KS tests, standard deviation, and feature importance. The authors\u0000also found that GAN works best for quantitative datasets.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139079383","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}
Dileepan JosephElectrical and Computer Engineering, University of Alberta
Model-based approaches to imaging, like specialized image enhancements in astronomy, favour physics-based models which facilitate explanations of relationships between observed inputs and computed outputs. While this paper features a tutorial example, inspired by exoplanet imaging, that reveals embedded 2D fast Fourier transforms in an image enhancement model, the work is actually about the tensor algebra and software, or tensor frameworks, available for model-based imaging. The paper proposes a Ricci-notation tensor (RT) framework, comprising an extended Ricci notation, which aligns well with the symbolic dual-index algebra of non-Euclidean geometry, and codesigned object-oriented software, called the RTToolbox for MATLAB. Extensions offer novel representations for entrywise, pagewise, and broadcasting operations popular in extended matrix-vector (EMV) frameworks for imaging. Complementing the EMV algebra computable with MATLAB, the RTToolbox demonstrates programmatic and computational efficiency thanks to careful design of tensor and dual-index classes. Compared to a numeric tensor predecessor, the RT framework enables superior ways to model imaging problems and, thereby, to develop solutions.
{"title":"Ricci-Notation Tensor Framework for Model-Based Approaches to Imaging","authors":"Dileepan JosephElectrical and Computer Engineering, University of Alberta","doi":"arxiv-2312.04018","DOIUrl":"https://doi.org/arxiv-2312.04018","url":null,"abstract":"Model-based approaches to imaging, like specialized image enhancements in\u0000astronomy, favour physics-based models which facilitate explanations of\u0000relationships between observed inputs and computed outputs. While this paper\u0000features a tutorial example, inspired by exoplanet imaging, that reveals\u0000embedded 2D fast Fourier transforms in an image enhancement model, the work is\u0000actually about the tensor algebra and software, or tensor frameworks, available\u0000for model-based imaging. The paper proposes a Ricci-notation tensor (RT)\u0000framework, comprising an extended Ricci notation, which aligns well with the\u0000symbolic dual-index algebra of non-Euclidean geometry, and codesigned\u0000object-oriented software, called the RTToolbox for MATLAB. Extensions offer\u0000novel representations for entrywise, pagewise, and broadcasting operations\u0000popular in extended matrix-vector (EMV) frameworks for imaging. Complementing\u0000the EMV algebra computable with MATLAB, the RTToolbox demonstrates programmatic\u0000and computational efficiency thanks to careful design of tensor and dual-index\u0000classes. Compared to a numeric tensor predecessor, the RT framework enables\u0000superior ways to model imaging problems and, thereby, to develop solutions.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138552293","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}
Benchmark sets are extremely important for evaluating and developing global optimization algorithms and related solvers. A new test set named PCC benchmark is proposed especially for optimization problem of nonlinear curve fitting for the first time, with the aspiration of investigating and comparing the performance of different global optimization solvers. Compared with the well-known classical nonlinear curve fitting benchmark set given by the National Institute of Standards and Technology (NIST) of USA, the most important features of the PCC benchmark are small problem dimensions, free search domain and high level of difficulty for obtaining global optimization solutions, which makes the PCC benchmark be not only suitable for validating the effectiveness of various global optimization algorithms, but also more ideal for verifying and comparing various solvers with global optimization solving capabilities. Based on PCC and NIST benchmark, seven of the world's leading global optimization solvers, including Baron, Antigone, Couenne, Lingo, Scip, Matlab GA and 1stOpt, are thoroughly tested and compared in terms of both effectiveness and efficiency. The results showed that the NIST benchmark is relatively simple and not suitable for global optimization testing, while the PCC benchmark is a unique, challengeable and effective test dataset for testing and verifying global optimization algorithms and related solvers. 1stOpt solver gives the overall best performance in both NIST and PCC benchmark.
{"title":"A New Challenging Curve Fitting Benchmark Test Set for Global Optimization Solvers","authors":"Peicong Cheng, Peicheng Cheng","doi":"arxiv-2312.01709","DOIUrl":"https://doi.org/arxiv-2312.01709","url":null,"abstract":"Benchmark sets are extremely important for evaluating and developing global\u0000optimization algorithms and related solvers. A new test set named PCC benchmark\u0000is proposed especially for optimization problem of nonlinear curve fitting for\u0000the first time, with the aspiration of investigating and comparing the\u0000performance of different global optimization solvers. Compared with the\u0000well-known classical nonlinear curve fitting benchmark set given by the\u0000National Institute of Standards and Technology (NIST) of USA, the most\u0000important features of the PCC benchmark are small problem dimensions, free\u0000search domain and high level of difficulty for obtaining global optimization\u0000solutions, which makes the PCC benchmark be not only suitable for validating\u0000the effectiveness of various global optimization algorithms, but also more\u0000ideal for verifying and comparing various solvers with global optimization\u0000solving capabilities. Based on PCC and NIST benchmark, seven of the world's\u0000leading global optimization solvers, including Baron, Antigone, Couenne, Lingo,\u0000Scip, Matlab GA and 1stOpt, are thoroughly tested and compared in terms of both\u0000effectiveness and efficiency. The results showed that the NIST benchmark is\u0000relatively simple and not suitable for global optimization testing, while the\u0000PCC benchmark is a unique, challengeable and effective test dataset for testing\u0000and verifying global optimization algorithms and related solvers. 1stOpt solver\u0000gives the overall best performance in both NIST and PCC benchmark.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"19 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138521074","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}
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