贝叶斯压缩感知论文(英文)
Speeded-Up-Robust-Features-SURF算法全文翻译
Speeded-Up Robust Features (SURF)Herbert Bay, Andreas Ess, Tinne Tuytelaars, Luc Van Gool摘要这篇文章提出了一种尺度和旋转不变的检测子和描述子，称为SURF(Speeded-Up Robust Features)。
SURF在可重复性、鉴别性和鲁棒性方面都接近甚至超过了以往的方案，同时计算和比较的速度更快。
这依赖于使用了积分图进行图像卷积、使用现有的最好的检测子和描述子〔特别是，基于Hessian矩阵方法的检测子，和基于分布的描述子〕、以及简化这些算法到了极致。
这些最终实现了新的检测、描述和匹配过程的结合。
本文包含对检测子和描述子的详细阐述，之后探究了一些关键参数的作用。
作为结论，我们用两个目标相反的应用测试了SURF的性能：摄像头校准〔图像配准的一个特列〕和目标识别。
我们的实验验证了SURF在电脑视觉广泛领域的实用性。
1.引言在两个图片中找到相似场景或目标的像素点一致性，这是许多电脑视觉应用中的一项任务。
图像配准，摄像头校准，目标识别，图像检索只是其中的一部分。
寻找离散像素点一致性的任务可以分为三步。
第一，选出兴趣点并分别标注在图像上，例如拐角、斑块和T型连接处。
兴趣点检测子最有价值的特性是可重复性。
可重复性说明的是检测子在不同视觉条件下找到相同真实兴趣点的能力。
然后，用特征向量描述兴趣点的邻域。
这个描述子应该有鉴别性，同时对噪声、位移、几何和光照变换具有鲁棒性。
最后，在不同的图片之间匹配特征向量。
这种匹配基于向量间的马氏或者欧氏距离。
描述子的维度对于计算时间有直接影响，对于快速兴趣点匹配，较小的维度是较好的。
然而，较小的特征向量维度也使得鉴别度低于高维特征向量。
我们的目标是开发新的检测子和描述子，相对于现有方案来说，计算速度更快，同时又不牺牲性能。
为了达成这一目标，我们必须在二者之间到达一个平衡，在保持精确性的前提下简化检测方案，在保持足够鉴别度的前提下减少描述子的大小。
人工智能英文参考文献(最新120个)
人工智能是一门新兴的具有挑战力的学科。
自人工智能诞生以来,发展迅速,产生了许多分支。
诸如强化学习、模拟环境、智能硬件、机器学习等。
但是,在当前人工智能技术迅猛发展,为人们的生活带来许多便利。
下面是搜索整理的人工智能英文参考文献的分享，供大家借鉴参考。
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Medicina,2020,80 Suppl 2.[109]Cong Lei,Feng Wanbing,Yao Zhigang,Zhou Xiaoming,Xiao Wei. Deep Learning Model as a New Trend in Computer-aided Diagnosis of Tumor Pathology for Lung Cancer.[J]. Journal of Cancer,2020,11(12).[110]Wang Fengdan,Gu Xiao,Chen Shi,Liu Yongliang,Shen Qing,Pan Hui,Shi Lei,Jin Zhengyu. Artificial intelligence system can achieve comparable results to experts for bone age assessment of Chinese children with abnormal growth and development.[J]. PeerJ,2020,8.[111]Hu Wenmo,Yang Huayu,Xu Haifeng,Mao Yilei. Radiomics based on artificial intelligence in liver diseases: where we are?[J]. Gastroenterology report,2020,8(2).[112]Batayneh Wafa,Abdulhay Enas,Alothman Mohammad. Prediction of the performance of artificial neural networks in mapping sEMG to finger joint angles via signal pre-investigation techniques.[J]. Heliyon,2020,6(4).[113]Aydin Emrah,Türkmen ?nan Utku,Namli G?zde,?ztürk ?i?dem,Esen Ay?e B,Eray Y Nur,Ero?lu Egemen,Akova Fatih. A novel and simple machine learning algorithm for preoperative diagnosis of acute appendicitis in children.[J]. Pediatric surgery international,2020.[114]Ellahham Samer. Artificial Intelligence in Diabetes Care.[J]. The Americanjournal of medicine,2020.[115]David J. Winkel,Thomas J. Weikert,Hanns-Christian Breit,Guillaume Chabin,Eli Gibson,Tobias J. Heye,Dorin Comaniciu,Daniel T. Boll. Validation of a fully automated liver segmentation algorithm using multi-scale deep reinforcement learning and comparison versus manual segmentation[J]. European Journal of Radiology,2020,126.[116]Binjie Fu,Guoshu Wang,Mingyue Wu,Wangjia Li,Yineng Zheng,Zhigang Chu,Fajin Lv. Influence of CT effective dose and convolution kernel on the detection of pulmonary nodules in different artificial intelligence software systems: A phantom study[J]. European Journal of Radiology,2020,126.[117]Georgios N. Kouziokas. A new W-SVM kernel combining PSO-neural network transformed vector and Bayesian optimized SVM in GDP forecasting[J]. Engineering Applications of Artificial Intelligence,2020,92.[118]Qingsong Ruan,Zilin Wang,Yaping Zhou,Dayong Lv. A new investor sentiment indicator ( ISI ) based on artificial intelligence: A powerful return predictor in China[J]. Economic Modelling,2020,88.[119]Mohamed Abdel-Basset,Weiping Ding,Laila Abdel-Fatah. The fusion of Internet of Intelligent Things (IoIT) in remote diagnosis of obstructive Sleep Apnea: A survey and a new model[J]. Information Fusion,2020,61.[120]Federico Caobelli. Artificial intelligence in medical imaging: Game over for radiologists?[J]. European Journal of Radiology,2020,126.以上就是关于人工智能参考文献的分享，希望对你有所帮助。
基于Nai
基于Naïve Bayes和TF—IDF的真假新闻分类作者：蔡扬付小斌来源：《电脑知识与技术》2018年第04期摘要：信息爆炸的时代，大量的新闻每天充斥的我们的生活，海量的新闻总是能够引导着人们对社会中发生的事件做出自己的判断。
假新闻的错误引导将会对社会起到消极的作用，于是该文提出对真假新闻进行分类的方法。
该文结合TF-IDF算法和朴素贝叶斯算法，对新闻中的词条进行加权，之后重新定义朴素贝叶斯分类器，并对新闻进行分类。
最后，我们进行了多组实验，并取得了多组实验的平均值作为本次实验的最终结论。
关键词：真假新闻；TF-IDF；朴素贝叶斯；分类中图分类号：TP181 文献标识码：A 文章编号：1009-3044（2018）04-0184-03Fake or Real News Classification Based on Naïve Bayes and TF-IDFCAI Yang， FU Xiao-bin（Southwest Petroleum University School of Computer Science， Chengdu 610500， China）Abstract：In this era of information explosion， a lot of news full of our lives every day，massive news is always able to guide people to the events of society to make their own judgments. The false guidance of false news will have a negative effect on society， so this paper proposes a method to classify true and false news. In this paper， we combined the TF-IDF algorithm and the naive Bayesian algorithm to weight the entries in the news， and then redefine the naive Bayesian classifier and classify the news. Finally， we conducted a number of experiments， and made the average of multiple sets of experiments as the final conclusion of this experiment.Key words： Fake or Real News；TF-IDF； Naïve Bayes； Classification新闻的真实性是新闻的立命的根本，但是近些年来，假新闻层出不尽，影响了新闻媒体的权威性和公信力；导致错误的舆论出现；侵害了公民的权利；浪费了时间和金钱，对社会造成了巨大的影响。
基于贝叶斯定理的数据稀疏表示与恢复研究
基于贝叶斯定理的数据稀疏表示与恢复研究随着科技的不断发展，数据科学已经成为了当今最为流行的领域之一。
而在数据科学领域中，数据稀疏表示与恢复技术可以说是一个非常重要而又有趣的研究方向。
近年来，基于贝叶斯定理的数据稀疏表示与恢复技术成为了研究的热点，本文旨在对这一领域进行探讨。
一、数据稀疏表示与恢复技术概述在数据科学领域中，数据稀疏表示指的是一种将高维数据表达为低维度表示的方法。
这种方法可以简化数据处理的过程，因为高维度数据在存储和计算上都会十分困难。
数据稀疏表示技术的一项重要任务是将稀疏信号从噪声之中恢复出来。
而恢复它的好处是可以帮助我们从噪声之中提取出有效的信息。
数据稀疏表示与恢复技术可以被广泛应用于数据压缩、图像处理、信号处理、模式识别、机器学习等众多领域。
这些领域中存在着大量的稀疏性，例如在自然图像或视频中，大量的元素都是无用的或者是无法提供有效信息的。
二、贝叶斯定理与数据稀疏表示贝叶斯定理是基于条件概率的一种数学方法，它能够帮助我们通过某些（已知或者假定的）条件概率来确定某些（未知的）概率。
在数据稀疏表示与恢复技术中，贝叶斯定理可以用来解决很多问题。
例如，它可以用来确定一个特定的向量在某个稀疏基中的系数值。
通过贝叶斯定理，我们可以使用先验概率分布来求出条件概率分布，这与统计学习中的贝叶斯估计是很相似的。
在某些数据稀疏表示问题中，我们需要确定一个稀疏表达式中向量中的系数值，而这样的问题就可以被看作是一种最优化问题，我们可以使用贝叶斯定理来求解该问题。
三、基于贝叶斯定理的数据稀疏表示与恢复算法基于贝叶斯定理的数据稀疏表示与恢复算法分为两个阶段：稀疏表示和恢复阶段。
在稀疏表示阶段，我们需要对原始数据进行稀疏编码，从而得到稀疏表示系数。
而在恢复阶段，我们则需要从稀疏表示中恢复出原始的数据。
下面我们介绍一些基于贝叶斯定理的数据稀疏表示与恢复算法。
1. FOCUSS算法FOCUSS算法是一种基于贝叶斯定理的数据稀疏表示与恢复算法。
范数规则化(L0,核范数等)
机器学习中的范数规则化之（一）L0、L1与L2范数zouxy09@ /zouxy09今天我们聊聊机器学习中出现的非常频繁的问题：过拟合与规则化。
我们先简单的来理解下常用的L0、L1、L2和核范数规则化。
最后聊下规则化项参数的选择问题。
这里因为篇幅比较庞大，为了不吓到大家，我将这个五个部分分成两篇博文。
知识有限，以下都是我一些浅显的看法，如果理解存在错误，希望大家不吝指正。
谢谢。
监督机器学习问题无非就是“minimize your error while regularizing your parameters”，也就是在规则化参数的同时最小化误差。
最小化误差是为了让我们的模型拟合我们的训练数据，而规则化参数是防止我们的模型过分拟合我们的训练数据。
多么简约的哲学啊！因为参数太多，会导致我们的模型复杂度上升，容易过拟合，也就是我们的训练误差会很小。
但训练误差小并不是我们的最终目标，我们的目标是希望模型的测试误差小，也就是能准确的预测新的样本。
所以，我们需要保证模型“简单”的基础上最小化训练误差，这样得到的参数才具有好的泛化性能（也就是测试误差也小），而模型“简单”就是通过规则函数来实现的。
另外，规则项的使用还可以约束我们的模型的特性。
这样就可以将人对这个模型的先验知识融入到模型的学习当中，强行地让学习到的模型具有人想要的特性，例如稀疏、低秩、平滑等等。
要知道，有时候人的先验是非常重要的。
前人的经验会让你少走很多弯路，这就是为什么我们平时学习最好找个大牛带带的原因。
一句点拨可以为我们拨开眼前乌云，还我们一片晴空万里，醍醐灌顶。
对机器学习也是一样，如果被我们人稍微点拨一下，它肯定能更快的学习相应的任务。
只是由于人和机器的交流目前还没有那么直接的方法，目前这个媒介只能由规则项来担当了。
还有几种角度来看待规则化的。
规则化符合奥卡姆剃刀(Occam's razor)原理。
这名字好霸气，razor！不过它的思想很平易近人：在所有可能选择的模型中，我们应该选择能够很好地解释已知数据并且十分简单的模型。
通信信号调制方式识别方法综述
通信信号调制方式识别方法综述曾创展;贾鑫;朱卫纲【摘要】对通信信号调制方式的识别进行了深入研究,对通信信号常用的数字调制技术和调制识别预处理技术、理想高斯白噪声条件下基于决策论和基于统计模式的识别法、非理想信道条件下的调制识别法以及对共信道多信号调制方式的识别等进行了总结.在简要介绍各种方法的来源、理论基础和发展基础上讨论了各自的优缺点,并提出了调制识别研究领域的进一步发展方向.【期刊名称】《通信技术》【年(卷),期】2015(048)003【总页数】6页(P252-257)【关键词】通信信号调制识别;基于决策论;基于统计模式;非理想信道条件下;共信道多信号【作者】曾创展;贾鑫;朱卫纲【作者单位】装备学院研究生管理大队,北京101416;装备学院光电装备系,北京101416;装备学院光电装备系,北京101416【正文语种】中文【中图分类】TN76;TN911调制识别通常位于接收机的前端，在信号检测和信号解调之间，接收方要根据信号的调制方式进行解调才能继续进行下一步操作直至最终获取信号携带的信息。
而在诸如无线电检测、侦察、对抗等应用中，侦察方通常缺乏足够的先验知识，如信号的调制参数、方式等，而为了达到区分信号来源、性质、内容等目的，就需要侦察方对信号的调制方式进行正确识别分类。
当前，制电磁权已日益成为重要的作战要素，战场电磁环境中存在着大量未知信号，此时人工识别已无法满足信号识别的实时性要求，因而，人们开始研究自动调制识别方法，1969年，C.S.Weaver等人就发表了第一篇关于自动调制识别方法研究的论文[1]，根据信号频谱的差异完成了自动识别。
随着通信信号从模拟调制发展为数字调制，调制方式更加复杂多样，调制识别算法的研究成果也越来越多，涉及方法体系也十分广泛。
本文从AWGN 条件下的调制识别、非理想信道条件下的调制识别以及共信道多信号的调制识别三方面概述了多种识别方法，在对各方法简要介绍的基础上对比讨论了各自的优缺点，展望了调制识别研究领域的进一步发展方向。
【国家自然科学基金】_贝叶斯优化算法_基金支持热词逐年推荐_【万方软件创新助手】_20140730
2012年 序号 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52
107 108 109 110 111 112 113 114 115
2011年 科研热词 贝叶斯网络 贝叶斯理论 贝叶斯方法 结构学习 遗传算法 贝叶斯优化算法 粒子群优化 分类 ls-svm k2算法 高斯过程 高光谱 马尔可夫链 风险评级 预测 非线性控制系统 降维 陆面过程模式 阈值选取 长尾分布 运动模糊 过程工艺优化 超拉普拉斯 贝叶斯网 贝叶斯模型平均 贝叶斯框架 贝叶斯推理 贝叶斯压缩感知 贝叶斯分类 贝叶斯准则 贝叶斯 观测器 覆冰闪络跳闸 行动过程 蚁群算法 蒙特卡洛 舞弊识别 自适应采样 自助抽样 脆弱性指标 统计学习 约束蚁群优化算法 系统生命周期 粒子群算法 粒子群优化算法 粒子群(pso) 簇头 算法 空间复用 神经网络 矽肺 目标检测 推荐指数 4 3 3 3 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2008年 序号 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
科研热词 贝叶斯网络 贝叶斯分类器 强化学习 增量学习 预测模型 遗传算法 退化现象 贝叶斯网分解 贝叶斯方法 舰船设备 结构学习 粒子群算法 粒子群优化 粒子滤波算法 简单贝叶斯 相关反馈 混合遗传算法 深度优先 水文地质参数 模式识别 朴素贝叶斯分类 广度优先 平行坐标 多智能体系统 多关系分类 多元数据 图像检索 参数识别 协同控制 动态贝叶斯网络 分类算法 公路交通 信息可视化 优化 交通状态 scam算法 q-学习 mcmc方法 irrl模型
基于BS-HMM和巴式距离的手势识别技术研究
基于BS-HMM和巴式距离的手势识别技术研究朱正伟;祝磊;饶鹏【摘要】开发一个基于深度图像的手势识别系统,将巴氏距离(Bhattacharyya distance)引入到贝叶斯感知隐马尔科夫模型(BS-HMM)中,称为BDBS-HMM.使用深度摄像机Kinect捕获深度序列图,通过骨架信息对手部位置进行跟踪,识别手部区域,得到手部分割图;从分割图像中提取4D曲面法线方向分布(HON4D)特征和方向梯度直方图(HOG)特征表示运动模式;将每后个连续的特征向量组合成一个序列分布变换所有训练特征向量,使用分布序列来对BDBS-HMM进行训练.该系统在使用MSRGesture3D数据库和自己建立的数据库的情况下,将BDBS-HMM与标准HMM和BS-HMM进行比较,实验结果表明了该系统的优越性.【期刊名称】《计算机应用与软件》【年(卷),期】2019(036)006【总页数】5页(P163-166,253)【关键词】手势识别;贝叶斯感知隐马尔科夫模型;巴氏距离;HON4D特征;HOG特征【作者】朱正伟;祝磊;饶鹏【作者单位】常州大学信息科学与工程学院江苏常州213164;常州大学信息科学与工程学院江苏常州213164;常州光电技术研究所江苏常州213164【正文语种】中文【中图分类】TP3910 引言手势识别交互技术是人机交互(HCI)研究的主要焦点之一。
目前，对于手势识别(HGR)的研究方法也比较多样化，这些方法可以根据所使用的传感器的不同进行分类[1]。
一般分为基于数据手套的手势识别和基于计算机视觉的手势识别，后者使人机交互更加自然，已经成为手势识别研究的重点。
本文提出了一种基于Kinect 深度传感器的手势识别系统，无需在用户身上穿戴任何外接设备。
基于Kinect深度传感器的手势识别研究大致分为手势分割、跟踪定位和特征提取三个过程。
Pisharady等[2]针对在复杂背景下手势分割不准确的问题，提出了一个多类手姿态的手势识别系统，并取得了较理想的效果。
基于吉布斯采样与压缩感知的二维非平稳CPT数据快速插值方法
基于吉布斯采样与压缩感知的二维非平稳CPT数据快速插值
方法
朱文清;赵腾远;宋超;王宇;许领
【期刊名称】《土木与环境工程学报(中英文)》
【年(卷),期】2022(44)5
【摘要】静力触探试验(Cone Penetration Test,CPT)常被用于确定地下土体分层情况及层内土体的力学参数等。
由于工期、工程投入、技术等条件限制,沿水平方向的CPT钻孔数目通常非常有限,有必要利用空间插值或随机模拟来估计未采样位置的CPT试验数据。
提出一种有效的蒙特卡洛方法,可直接根据有限的CPT试验钻孔数据估计未采样位置的CPT数据,该方法将二维贝叶斯压缩感知框架与吉布斯采样相结合,并引入克罗内克积以提高其计算效率,然后用一系列数值及实际工程案例验证了所提方法的可靠性。
结果表明:该插值方法合理,不仅能如实反映数据本身的非平稳特点,且采用序列更新技术后可显著降低时间成本,具有更强的适应能力。
此外,插值结果的准确性、可靠性与已有CPT钻孔的距离成反比、与已有钻孔的数目成正比,反映出方法本身数据驱动的特点。
【总页数】11页(P98-108)
【作者】朱文清;赵腾远;宋超;王宇;许领
【作者单位】西安科技大学地质与环境学院;西安交通大学人居环境与建筑工程学院;香港城市大学建筑学及土木工程学系
【正文语种】中文
【中图分类】TU413.3
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2.基于吉布斯采样结果的主题文本网络构建方法
3.基于吉布斯采样的TFBS识别算法研究
4.基于吉布斯抽样的相关观测异常值检测的贝叶斯方法
5.表驱动的二维非规则采样快速傅里叶变换
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卷积神经网络机器学习外文文献翻译中英文2020
卷积神经网络机器学习相关外文翻译中英文2020英文Prediction of composite microstructure stress-strain curves usingconvolutional neural networksCharles Yang，Youngsoo Kim，Seunghwa Ryu，Grace GuAbstractStress-strain curves are an important representation of a material's mechanical properties, from which important properties such as elastic modulus, strength, and toughness, are defined. However, generating stress-strain curves from numerical methods such as finite element method (FEM) is computationally intensive, especially when considering the entire failure path for a material. As a result, it is difficult to perform high throughput computational design of materials with large design spaces, especially when considering mechanical responses beyond the elastic limit. In this work, a combination of principal component analysis (PCA) and convolutional neural networks (CNN) are used to predict the entire stress-strain behavior of binary composites evaluated over the entire failure path, motivated by the significantly faster inference speed of empirical models. We show that PCA transforms the stress-strain curves into an effective latent space by visualizing the eigenbasis of PCA. Despite having a dataset of only 10-27% of possible microstructure configurations, the mean absolute error of the prediction is <10% of therange of values in the dataset, when measuring model performance based on derived material descriptors, such as modulus, strength, and toughness. Our study demonstrates the potential to use machine learning to accelerate material design, characterization, and optimization.Keywords：Machine learning，Convolutional neural networks，Mechanical properties，Microstructure，Computational mechanics IntroductionUnderstanding the relationship between structure and property for materials is a seminal problem in material science, with significant applications for designing next-generation materials. A primary motivating example is designing composite microstructures for load-bearing applications, as composites offer advantageously high specific strength and specific toughness. Recent advancements in additive manufacturing have facilitated the fabrication of complex composite structures, and as a result, a variety of complex designs have been fabricated and tested via 3D-printing methods. While more advanced manufacturing techniques are opening up unprecedented opportunities for advanced materials and novel functionalities, identifying microstructures with desirable properties is a difficult optimization problem.One method of identifying optimal composite designs is by constructing analytical theories. For conventional particulate/fiber-reinforced composites, a variety of homogenizationtheories have been developed to predict the mechanical properties of composites as a function of volume fraction, aspect ratio, and orientation distribution of reinforcements. Because many natural composites, synthesized via self-assembly processes, have relatively periodic and regular structures, their mechanical properties can be predicted if the load transfer mechanism of a representative unit cell and the role of the self-similar hierarchical structure are understood. However, the applicability of analytical theories is limited in quantitatively predicting composite properties beyond the elastic limit in the presence of defects, because such theories rely on the concept of representative volume element (RVE), a statistical representation of material properties, whereas the strength and failure is determined by the weakest defect in the entire sample domain. Numerical modeling based on finite element methods (FEM) can complement analytical methods for predicting inelastic properties such as strength and toughness modulus (referred to as toughness, hereafter) which can only be obtained from full stress-strain curves.However, numerical schemes capable of modeling the initiation and propagation of the curvilinear cracks, such as the crack phase field model, are computationally expensive and time-consuming because a very fine mesh is required to accommodate highly concentrated stress field near crack tip and the rapid variation of damage parameter near diffusive cracksurface. Meanwhile, analytical models require significant human effort and domain expertise and fail to generalize to similar domain problems.In order to identify high-performing composites in the midst of large design spaces within realistic time-frames, we need models that can rapidly describe the mechanical properties of complex systems and be generalized easily to analogous systems. Machine learning offers the benefit of extremely fast inference times and requires only training data to learn relationships between inputs and outputs e.g., composite microstructures and their mechanical properties. Machine learning has already been applied to speed up the optimization of several different physical systems, including graphene kirigami cuts, fine-tuning spin qubit parameters, and probe microscopy tuning. Such models do not require significant human intervention or knowledge, learn relationships efficiently relative to the input design space, and can be generalized to different systems.In this paper, we utilize a combination of principal component analysis (PCA) and convolutional neural networks (CNN) to predict the entire stress-strain c urve of composite failures beyond the elastic limit. Stress-strain curves are chosen as the model's target because t hey are difficult to predict given their high dimensionality. In addition, stress-strain curves are used to derive important material descriptors such as modulus, strength, and toughness. In this sense, predicting stress-straincurves is a more general description of composites properties than any combination of scaler material descriptors. A dataset of 100,000 different composite microstructures and their corresponding stress-strain curves are used to train and evaluate model performance. Due to the high dimensionality of the stress-strain dataset, several dimensionality reduction methods are used, including PCA, featuring a blend of domain understanding and traditional machine learning, to simplify the problem without loss of generality for the model.We will first describe our modeling methodology and the parameters of our finite-element method (FEM) used to generate data. Visualizations of the learned PCA latent space are then presented, a long with model performance results.CNN implementation and trainingA convolutional neural network was trained to predict this lower dimensional representation of the stress vector. The input to the CNN was a binary matrix representing the composite design, with 0's corresponding to soft blocks and 1's corresponding to stiff blocks. PCA was implemented with the open-source Python package scikit-learn, using the default hyperparameters. CNN was implemented using Keras with a TensorFlow backend. The batch size for all experiments was set to 16 and the number of epochs to 30; the Adam optimizer was used to update the CNN weights during backpropagation.A train/test split ratio of 95:5 is used –we justify using a smaller ratio than the standard 80:20 because of a relatively large dataset. With a ratio of 95:5 and a dataset with 100,000 instances, the test set size still has enough data points, roughly several thousands, for its results to generalize. Each column of the target PCA-representation was normalized to have a mean of 0 and a standard deviation of 1 to prevent instable training.Finite element method data generationFEM was used to generate training data for the CNN model. Although initially obtained training data is compute-intensive, it takes much less time to train the CNN model and even less time to make high-throughput inferences over thousands of new, randomly generated composites. The crack phase field solver was based on the hybrid formulation for the quasi-static fracture of elastic solids and implementedin the commercial FEM software ABAQUS with a user-element subroutine (UEL).Visualizing PCAIn order to better understand the role PCA plays in effectively capturing the information contained in stress-strain curves, the principal component representation of stress-strain curves is plotted in 3 dimensions. Specifically, we take the first three principal components, which have a cumulative explained variance ~85%, and plot stress-strain curves in that basis and provide several different angles from which toview the 3D plot. Each point represents a stress-strain curve in the PCA latent space and is colored based on the associated modulus value. it seems that the PCA is able to spread out the curves in the latent space based on modulus values, which suggests that this is a useful latent space for CNN to make predictions in.CNN model design and performanceOur CNN was a fully convolutional neural network i.e. the only dense layer was the output layer. All convolution layers used 16 filters with a stride of 1, with a LeakyReLU activation followed by BatchNormalization. The first 3 Conv blocks did not have 2D MaxPooling, followed by 9 conv blocks which did have a 2D MaxPooling layer, placed after the BatchNormalization layer. A GlobalAveragePooling was used to reduce the dimensionality of the output tensor from the sequential convolution blocks and the final output layer was a Dense layer with 15 nodes, where each node corresponded to a principal component. In total, our model had 26,319 trainable weights.Our architecture was motivated by the recent development and convergence onto fully-convolutional architectures for traditional computer vision applications, where convolutions are empirically observed to be more efficient and stable for learning as opposed to dense layers. In addition, in our previous work, we had shown that CNN's werea capable architecture for learning to predict mechanical properties of 2Dcomposites [30]. The convolution operation is an intuitively good fit forpredicting crack propagation because it is a local operation, allowing it toimplicitly featurize and learn the local spatial effects of crack propagation.After applying PCA transformation to reduce the dimensionality ofthe target variable, CNN is used to predict the PCA representation of thestress-strain curve of a given binary composite design. After training theCNN on a training set, its ability to generalize to composite designs it hasnot seen is evaluated by comparing its predictions on an unseen test set.However, a natural question that emerges i s how to evaluate a model's performance at predicting stress-strain curves in a real-world engineeringcontext. While simple scaler metrics such as mean squared error (MSE)and mean absolute error (MAE) generalize easily to vector targets, it isnot clear how to interpret these aggregate summaries of performance. It isdifficult to use such metrics to ask questions such as “Is this modeand “On average, how poorly will aenough to use in the real world” given prediction be incorrect relative to some given specification”. Although being able to predict stress-strain curves is an importantapplication of FEM and a highly desirable property for any machinelearning model to learn, it does not easily lend itself to interpretation. Specifically, there is no simple quantitative way to define whether two-world units.stress-s train curves are “close” or “similar” with real Given that stress-strain curves are oftentimes intermediary representations of a composite property that are used to derive more meaningful descriptors such as modulus, strength, and toughness, we decided to evaluate the model in an analogous fashion. The CNN prediction in the PCA latent space representation is transformed back to a stress-strain curve using PCA, and used to derive the predicted modulus, strength, and toughness of the composite. The predicted material descriptors are then compared with the actual material descriptors. In this way, MSE and MAE now have clearly interpretable units and meanings. The average performance of the model with respect to the error between the actual and predicted material descriptor values derived from stress-strain curves are presented in Table. The MAE for material descriptors provides an easily interpretable metric of model performance and can easily be used in any design specification to provide confidence estimates of a model prediction. When comparing the mean absolute error (MAE) to the range of values taken on by the distribution of material descriptors, we can see that the MAE is relatively small compared to the range. The MAE compared to the range is <10% for all material descriptors. Relatively tight confidence intervals on the error indicate that this model architecture is stable, the model performance is not heavily dependent on initialization, and that our results are robust to differenttrain-test splits of the data.Future workFuture work includes combining empirical models with optimization algorithms, such as gradient-based methods, to identify composite designs that yield complementary mechanical properties. The ability of a trained empirical model to make high-throughput predictions over designs it has never seen before allows for large parameter space optimization that would be computationally infeasible for FEM. In addition, we plan to explore different visualizations of empirical models-box” of such models. Applying machine in an effort to “open up the blacklearning to finite-element methods is a rapidly growing field with the potential to discover novel next-generation materials tailored for a variety of applications. We also note that the proposed method can be readily applied to predict other physical properties represented in a similar vectorized format, such as electron/phonon density of states, and sound/light absorption spectrum.ConclusionIn conclusion, we applied PCA and CNN to rapidly and accurately predict the stress-strain curves of composites beyond the elastic limit. In doing so, several novel methodological approaches were developed, including using the derived material descriptors from the stress-strain curves as interpretable metrics for model performance and dimensionalityreduction techniques to stress-strain curves. This method has the potential to enable composite design with respect to mechanical response beyond the elastic limit, which was previously computationally infeasible, and can generalize easily to related problems outside of microstructural design for enhancing mechanical properties.中文基于卷积神经网络的复合材料微结构应力-应变曲线预测查尔斯，吉姆，瑞恩，格瑞斯摘要应力-应变曲线是材料机械性能的重要代表，从中可以定义重要的性能，例如弹性模量，强度和韧性。
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1BayesianCompressiveSensing
ShihaoJi,YaXue,andLawrenceCarinDepartmentofElectricalandComputerEngineeringDukeUniversity,Durham,NC27708-0291USA{shji,yx10,lcarin}@ece.duke.eduEDICS:DSP-RECO,MAL-BAYL
AbstractThedataofinterestareassumedtoberepresentedasN-dimensionalrealvectors,andthesevectorsarecompressibleinsomelinearbasisB,implyingthatthesignalcanbereconstructedaccuratelyusingonlyasmallnumberMNofbasis-functioncoefficientsassociatedwithB.CompressivesensingisaframeworkwherebyonedoesnotmeasureoneoftheaforementionedN-dimensionalsignalsdirectly,butratherasetofrelatedmeasurements,withthenewmeasurementsalinearcombinationoftheoriginalunderlyingN-dimensionalsignal.Thenumberofrequiredcompressive-sensingmeasurementsistypicallymuchsmallerthanN,offeringthepotentialtosimplifythesensingsystem.LetfdenotetheunknownunderlyingN-dimensionalsignal,andgavectorofcompressive-sensingmeasurements,thenonemayapproximatefaccuratelybyutilizingknowledgeofthe(under-determined)linearrelationshipbetweenfandg,inadditiontoknowledgeofthefactthatfiscompressibleinB.InthispaperweemployaBayesianformalismforestimatingtheunderlyingsignalfbasedoncompressive-sensingmeasurementsg.Theproposedframeworkhasthefollowingproperties:(i)inadditiontoestimatingtheunderlyingsignalf,“errorbars”arealsoestimated,thesegivingameasureofconfidenceintheinvertedsignal;(ii)usingknowledgeoftheerrorbars,aprincipledmeansisprovidedfordeterminingwhenasufficientnumberofcompressive-sensingmeasurementshavebeenperformed;(iii)thissettinglendsitselfnaturallytoaframeworkwherebythecompressivesensingmeasurementsareoptimizedadaptivelyandhencenotdeterminedrandomly;and(iv)theframeworkaccountsforadditivenoiseinthecompressive-sensingmeasurementsandprovidesanestimateofthenoisevariance.Inthispaperwepresenttheunderlyingtheory,anassociatedalgorithm,exampleresults,andprovidecomparisonstoothercompressive-sensinginversionalgorithmsintheliterature.
IndexTermsCompressivesensing(CS),SparseBayesianlearning,Relevancevectormachine(RVM),Experimen-taldesign,Adaptivecompressivesensing,Bayesianmodelselection.
October27,2007DRAFT2I.INTRODUCTION
Overthelasttwodecadestherehavebeensignificantadvancesinthedevelopmentoforthonormalbasesforcompactrepresentationofawideclassofdiscretesignals.Animportantexampleofthisisthewavelettransform[1],[2],withwhichgeneralsignalsarerepresentedintermsofatomicelementslocalizedintimeandfrequency,assumingthatthedataindexrepresentstime(itmaysimilarlyrepresentspace).Thelocalizedpropertiesoftheseorthonormaltime-frequencyatomsyieldshighlycompactrepresentationsofmanynaturalsignals[1],[2].LettheN×NmatrixBrepresentawaveletbasis,withbasisfunctionsdefinedbyassociatedcolumns;ageneralsignalf∈RNmayberepresentedasf=Bw,wherew∈RNrepresentsthewaveletandscalingfunctioncoefficients[1],[2].Formostnaturalsignalsf,mostcomponentsofthevectorwhavenegligibleamplitude.Therefore,ifˆwrepresentstheweightsw
withthesmallestN−Mcoefficientssettozero,andˆf=Bˆw,thentherelativeerrorf−ˆf2/f
2
isoftennegligiblysmallforMN.Thispropertyhasledtothedevelopmentofstate-of-the-art
compressionalgorithmsbasedonwavelet-basedtransformcoding[3],[4].InconventionalapplicationsonefirstmeasurestheN-dimensionalsignalf,fisthencompressed(oftenusingawavelet-basedtransformcodingscheme),andthecompressedsetofbasis-functioncoefficientswarestoredinbinary[3],[4].Thisinvitesthefollowingquestion:Iftheunderlyingsignalisultimatelycompressible,isitpossibletoperformacompact(“compressive”)setofmeasurementsdirectly,therebyofferingthepotentialtosimplifythesensingsystem(reducethenumberofrequiredmeasurements)?Thisquestionhasrecentlybeenansweredintheaffirmative[5],[6],introducingthefieldofcompressivesensing(CS).InitsearliestformtherelationshipbetweentheunderlyingsignalfandtheCSmeasurementsghasbeenconstitutedthroughrandomprojections[6],[7].Specifically,assumethatthesignalfiscompressibleinsomebasisB(notnecessarilyawaveletbasis),thek-thCSmeasurementgk(k-thcomponentofg)isconstitutedbyprojectingfontoa“random”basisthatisconstitutedwith“random”linearcombinationofthebasisfunctionsinB,i.e.,gk=fT(Brk),whererk∈RNisacolumnvectorwitheachelementani.i.d.drawofarandomvariable,witharbitraryalphabet(e.g.,realorbinary)[6],[7].Basedontheabovediscussion,theCSmeasurementsmayberepresentedasg=ΦBTf=Φw,whereΦ=[r1...rK]TisaK×Nmatrix,assumingKrandomCSmeasurementsaremade.SincetypicallyKTherefore,inversionfortheN-weightsrepresentedbyw(andhencef)isill-posed.However,ifoneexploitsthefactthatwissparsewithrespecttoaknownorthonormalbasisB,thenonemayapproximate