检索结果-内蒙古大学图书馆

作者： Ko, Taehee The Pennsylvania State University

学位级别：Ph.D., Doctor of Philosophy

Modern machine learning has drawn a lot of attention from many researchers, showing promising directions where some of large-scale computational challenges become tractable, especially in material science and chemistry. In this dissertation, we explore several problems in computational chemistry and machine learning in the perspective of mathematics. We develop stochastic algorithms supplemented with rigorous analysis, especially for self-consistent computations in electronic structure theory. We also present a local convergence analysis of the stochastic gradient descent algorithms for non-convex models in machine learning. Lastly, we demonstrate the effectiveness of the diffusion map to ab-initio molecular dynamics data for identifying reaction collective variables and computing committor ***-consistent calculations of electronic structure have recently become routine computations for many applications such as the analysis of material properties and the simulation of molecular dynamics [33, 70, 87, 88, 90, 103, 117, 126]. The computational cost of standard self-consistent calculations increases cubically with respect to system size (e.g. density functional theory (DFT) [4, 55, 68, 70, 120] or self-consistent charge density functional tight-binding (SCC-DFTB) [33] ). The quantities of interest in DFT and SCC-DFTB are determined by the electron charges, which can be formulated as a diagonal of a matrix function. Many numerical methods have been proposed to speed up self-consistent calculations [3, 14–16, 18, 19, 35, 51, 59, 69, 81, 105, 132, 135, 136]. However, standard self-consistent calculations for computing electron charges require the eigenvalues and eigenvectors of such a matrix function, which makes those calculations intractable for large electronic systems. Chapter 1 of this dissertation presents a stochastic framework for the self-consistent calculations, which formulates the electron charges as a conditional expectation using the diagonal esti

关键词： Machine learning stochastic algorithms Large electronic systems

来源：评论

学校读者我要写书评

暂无评论

Estimation of Systemic Shortfall Risk Measure Using stochastic algorithms

引用

SIAM JOURNAL ON FINANCIAL MATHEMATICS 2024年第3期15卷 700-733页

作者： Kaakai, Sarah Matoussi, Anis Tamtalini, Achraf Le Mans Univ Inst Risque & Assurance Lab Manceau Math Le Mans France Le Mans Univ Inst Risque & Assurance FR CNRS 2962 Le Mans France Ecole Polytech Ctr Math Appl CNRS Palaiseau France

Systemic risk measures were introduced to capture the global risk and the corresponding contagion effects that are generated by an interconnected system of financial institutions. To this purpose, two approaches were suggested. In the first one, systemic risk measures can be interpreted as the minimal amount of cash needed to secure a system after aggregating individual risks. In the second approach, systemic risk measures can be interpreted as the minimal amount of cash that secures a system by allocating capital to each single institution before aggregating individual risks. Although the theory behind these risk measures has been well investigated by several authors, the numerical part has been neglected so far. In this paper, we use stochastic algorithms schemes in estimating multivariate shortfall risk measure and prove that the resulting estimators are consistent and asymptotically normal. We also test numerically the performance of these algorithms on several examples.

关键词： multivariate risk measures shortfall risk stochastic algorithms stochastic root finding risk allocations

来源：评论

学校读者我要写书评

暂无评论

Advancing Sustainable Energy: Analyzing stochastic algorithms and Q-Learning for Wind Farm Layout Optimization 5

Advancing Sustainable Energy: Analyzing Stochastic Algorithm...

引用

5th International Conference on Artificial Intelligence, Robotics and Control (AIRC)

作者： Elsheikh, Mohamed Yonis, Amr Magdy, Jessica Shehata, Omar M. German Univ Cairo Comp Sci Dept Fac Media Engn & Technol Cairo Egypt German Univ Cairo Mechatron Engn Dept Fac Engn & Mat Sci Cairo Egypt Multirobot Syst MRS Res Grp Cairo Egypt

ISBN: (纸本)9798350385083;9798350385076

This paper presents a comprehensive study on the optimization of wind farm layouts, a critical aspect of enhancing the efficiency and effectiveness of wind energy production. We delve into various optimization techniques, including Simulated Annealing, Genetic Algorithm, Particle Swarm Optimization, Moth Flame Optimization, and Deep Q-Learning. Each optimization technique is explored through a series of case studies, where different configurations and parameters are applied to assess their effectiveness in optimizing wind farm layouts. These techniques are evaluated based on criteria such as computational complexity, optimality of solutions, and repeatability of results. The paper's findings offer insightful comparisons and analyses of each technique, providing an understanding of their respective strengths and limitations in the context of wind farm layout optimization.

关键词： Sustainable Energy Wind Farm Layout Optimization Meta-Heuristic stochastic algorithms Multi-Cooperative Systems Simulated Annealing Genetic Algorithm Particle Swarm Moth Flame Reinforcement Learning Q-Learning

来源：评论

学校读者我要写书评

暂无评论

Non-Asymptotic Analysis of stochastic Approximation algorithms for Streaming Data

引用

ESAIM-PROBABILITY AND STATISTICS 2023年 27卷 482-514页

作者： Godichon-Baggioni, Antoine Werge, Nicklas Wintenberger, Olivier Sorbonne Univ Lab Probabil Stat & Modelisat LPSM F-75005 Paris France Univ Wien Wolfgang Pauli Inst Fak Math A-1090 Vienna Austria

We introduce a streaming framework for analyzing stochastic approximation/optimization problems. This streaming framework is analogous to solving optimization problems using time-varying mini-batches that arrive sequentially. We provide non-asymptotic convergence rates of various gradientbased algorithms;this includes the famous stochastic Gradient (SG) descent (a.k.a. Robbins-Monro algorithm), mini-batch SG and time-varying mini-batch SG algorithms, as well as their iterated averages (a.k.a. Polyak-Ruppert averaging). We show (i) how to accelerate convergence by choosing the learning rate according to the time-varying mini-batches, (ii) that Polyak-Ruppert averaging achieves optimal convergence in terms of attaining the Cramer-Rao lower bound, and (iii) how time-varying mini-batches together with Polyak-Ruppert averaging can provide variance reduction and accelerate convergence simultaneously, which is advantageous for many learning problems, such as online, sequential, and large-scale learning. We further demonstrate these favorable effects for various time-varying minibatches.

关键词： stochastic algorithms stochastic optimization machine learning online learning mini-batch streaming

来源：评论

学校读者我要写书评

暂无评论

Optimization of heat transfer in a grooved pipe model by stochastic algorithms and DOE based RSM

引用

INTERNATIONAL JOURNAL OF THERMAL SCIENCES 2021年 159卷 106634-106634页

作者： Gungor, Sahin Ceyhan, Umut Karadeniz, Ziya Haktan Izmir Katip Celebi Univ Dept Mech Engn TR-35620 Izmir Turkey

Additive manufacturing is a promising candidate to eliminate design constraints in thermal-fluid engineering problems as it enables optimized free-form designs to be produced. The brute force optimization needs too many experiments and/or analyses to obtain an optimized design. However, the same engineering design can be achieved by fewer experiments by using design of experiment (DOE) methodology, which minimizes the work load. In this study, local and mean heat transfer coefficients for a grooved pipe model are optimized and the system constraints are determined in compatible with the additive manufacturing method. DOE based response surface methodology (RSM) and an in-house developed optimization code are used to obtain the optimal local and mean heat transfer coefficients. The analyses are performed for both laminar and turbulent flow cases for understanding the backward and forward effects of grove dimensions better. The comparison of the recirculation regions in the groove geometries for optimal cases of laminar and turbulent flows reveals that the grooves in the pipe do not have to be uniform along the streamwise direction to obtain optimal heat transfer for local needs. This optimization approach provides both local and global controllability of heat transfer and the heat transfer values can be increased up to 20% in this thermal-fluid engineering problem. In addition, pressure drop and heat transfer contribution ratio of each grooved section are presented in detail.

关键词： Heat transfer optimization Design of experiments Response surface methodology Additive manufacturing stochastic algorithms

来源：评论

学校读者我要写书评

暂无评论

On stochastic evolving algorithms 22

On stochastic evolving algorithms

引用

Genetic and Evolutionary Computation Conference (GECCO)

作者： Fister, Iztok, Jr. Fister, Iztok Univ Maribor Maribor Slovenia

ISBN: (纸本)9781450392686

This pioneering study tries to break the wall of the question, how to develop algorithms capable of self-improving. The foundation of this work is the extended model of the human mind, while the information flow between components is inspired by molecular genetics. As a result, the proposed evolving algorithms consist of complex rules and stochastic processing, while the preliminary results also revealed enormous potential for the future.

关键词： evolving algorithms cognitive model stochastic algorithms

来源：评论

学校读者我要写书评

暂无评论

ACCELERATED stochastic algorithms FOR NONCONVEX FINITE-SUM AND MULTIBLOCK OPTIMIZATION

引用

SIAM JOURNAL ON OPTIMIZATION 2019年第4期29卷 2753-2784页

作者： Lan, Guanghui Yang, Yu Georgia Inst Technol H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA

In this paper, we present new stochastic methods for solving two important classes of nonconvex optimization problems. We first introduce a randomized accelerated proximal gradient (RapGrad) method for solving a class of nonconvex optimization problems whose objective function consists of the summation of m components and show that it can significantly reduce the number of gradient computations especially when the condition number L/mu (i.e., the ratio between the Lipschitz constant and negative curvature) is large. More specifically, RapGrad can save up to O(root m) gradient computations more than existing batch nonconvex accelerated gradient methods. Moreover, the number of gradient computations required by RapGrad can be O(m(1/6)L(1/2)/mu(1/2)) (at least O(m(2/3))) times smaller than the best-known randomized nonconvex gradient methods when L/mu >= m. Inspired by RapGrad, we also develop a new randomized accelerated proximal dual (RapDual) method for solving a class of multiblock nonconvex optimization problems coupled with linear constraints and some special structural properties. We demonstrate that RapDual can also save up to a factor of O(root m) block updates more than its batch counterpart, where m denotes the number of blocks. To the best of our knowledge, all these complexity results associated with RapGrad and RapDual seem to be new in the literature. We also illustrate potential advantages of these algorithms through our preliminary numerical experiments.

关键词： nonconvex optimization stochastic algorithms acceleration finite-sum optimization multiblock optimization

来源：评论

学校读者我要写书评

暂无评论

ARTIFICIAL INTELLIGENCE AND stochastic OPTIMIZATION algorithms FOR THE CHAOTIC DATASETS

引用

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY 2023年第6期31卷 2240175-2240175页

作者： Wang, Fuzhang Sohail, Ayesha Wong, Wing-Keung Azim, Qurat Ul Ain Farwa, Shabieh Sajad, Maria Nanchang Inst Technol Nanchang 330044 Peoples R China Xuzhou Univ Technol Sch Math & Stat Xuzhou 2221018 Jiangsu Peoples R China COMSATS Univ Islamabad Dept Math Lahore Campus Islamabad 54000 Pakistan Asia Univ FinTech & Blockchain Res Ctr Dept Finance Taichung Taiwan Asia Univ Big Data Res Ctr Taichung Taiwan China Med Univ Hosp Dept Med Res Yude Rd Taichung 404327 Taiwan Hang Seng Univ Hong Kong Dept Econ & Finance Hong Kong Peoples R China COMSATS Univ Islamabad Dept Math WahCant CampusMall RdQuaid Ave Rawalpindi Punjab Pakistan

Almost every natural process is stochastic due to the basic consequences of nature's existence and the dynamical behavior of each process that is not stationary but evolves with the passage of time. These stochastic processes not only exist and appear in the fields of biological sciences but are also evident in industrial, agricultural and economical research datasets. stochastic processes are challenging to model and to solve as well. The stochastic patterns when repeated result into random fractals and are very common in natural processes. These processes are usually simulated with the aid of smart computational and optimization tools. With the progress in the field of artificial intelligence, smart tools are developed that can model the stochastic processes by generalization and genetic optimization. Based on the basic theoretical description of the stochastic optimization algorithms, the stochastic learning tools, stochastic modeling, stochastic approximation and stochastic fractals, a comparative analysis is presented with the aid of the stochastic fractal search, multi-objective stochastic fractal search and pattern search algorithms.

关键词： stochastic Machine Learning Tools stochastic algorithms Genetic algorithms stochastic Fractal Search Imaging Data Analysis

来源：评论

学校读者我要写书评

暂无评论

Deep Statistical Comparison for Multi-Objective stochastic Optimization algorithms

引用

SWARM AND EVOLUTIONARY COMPUTATION 2021年 61卷

作者： Eftimov, Tome Korosec, Peter Jozef Stefan Inst Comp Syst Dept Jamova Cesta 39 Ljubljana 1000 Slovenia

Making a statistical comparison of meta-heuristic multi-objective optimization algorithms is crucial for identifying the strengths and weaknesses of a newly proposed algorithm. Currently, state-of-the-art comparison approaches involve user-preference-based selection of a single quality indicator or an ensemble of quality indicators as a comparison metric. Using these quality indicators, high-dimensional data is transformed into one-dimensional data. By doing this, information contained in the high-dimensional space can be lost, which will affect the results of the comparison. To avoid losing this information, we propose a novel ranking scheme that compares the distributions of high-dimensional data. Experimental results show that the proposed approach reduces potential information loss when statistical significance is not observed in high-dimensional data. Consequently, the selection of a quality indicator is required only in cases when statistical significance is observed in high-dimensional data. With this the cases that are affected by the user preference selection are reduced.

关键词： statistical comparison multi-objective problems stochastic algorithms benchmarking high-dimensional data

来源：评论

学校读者我要写书评

暂无评论

Benchmarking stochastic algorithms for Global Optimization Problems by Visualizing Confidence Intervals

引用

IEEE TRANSACTIONS ON CYBERNETICS 2017年第9期47卷 2924-2937页

作者： Liu, Qunfeng Chen, Wei-Neng Deng, Jeremiah D. Gu, Tianlong Zhang, Huaxiang Yu, Zhengtao Zhang, Jun Dongguan Univ Technol Sch Comp Sci & Network Secur Dongguan 523808 Peoples R China South China Univ Technol Sch Comp Sci & Engn Guangzhou 510006 Guangdong Peoples R China Univ Otago Dept Informat Sci Dunedin 9054 New Zealand Guilin Univ Elect Technol Sch Comp Sci & Engn Guilin 541004 Peoples R China Shandong Normal Univ Sch Informat Sci & Engn Jinan 250014 Shandong Peoples R China Kunming Univ Sci & Technol Sch Informat Engn & Automat Kunming 650500 Yunnan Peoples R China

The popular performance profiles and data profiles for benchmarking deterministic optimization algorithms are extended to benchmark stochastic algorithms for global optimization problems. A general confidence interval is employed to replace the significance test, which is popular in traditional benchmarking methods but suffering more and more criticisms. Through computing confidence bounds of the general confidence interval and visualizing them with performance profiles and (or) data profiles, our benchmarking method can be used to compare stochastic optimization algorithms by graphs. Compared with traditional benchmarking methods, our method is synthetic statistically and therefore is suitable for large sets of benchmark problems. Compared with some sample-mean-based benchmarking methods, e.g., the method adopted in black-boxoptimization-benchmarking workshop/competition, our method considers not only sample means but also sample variances. The most important property of our method is that it is a distribution-free method, i.e., it does not depend on any distribution assumption of the population. This makes it a promising benchmarking method for stochastic optimization algorithms. Some examples are provided to illustrate how to use our method to compare stochastic optimization algorithms.

关键词： Benchmarking computational budget evolutionary algorithms global optimization performance comparison stochastic algorithms

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：