检索结果-内蒙古大学图书馆

Riemannian-based neural network method for solving canonical correlation analysis

COMPUTATIONAL & APPLIED MATHEMATICS 2025年第5期44卷 1-16页

作者： Xie, Zhuo-Cheng Wang, Ming Wang, Yu-Hang Ren, Huan Jiangxi Sci & Technol Normal Univ Sch Math Sci Nanchang 330038 Peoples R China

Canonical correlation analysis is a classic statistical technique. In this paper, we develop a neural network method based on the Riemannian gradient for solving canonical correlation analysis problems. For the theoretical analysis, the geometric dynamics properties of this method are investigated. Numerical experiments indicate the feasibility and effectiveness of the proposed neural network method.

关键词： Canonical correlation analysis neural network method Generalized Stiefel manifold Riemannian gradient

来源：评论

学校读者我要写书评

暂无评论

neural network method for solving nonlinear fractional advection-diffusion equation with spatiotemporal variable-order

引用

CHAOS SOLITONS & FRACTALS 2022年 156卷 111856-111856页

作者： Qu, Hai-Dong Liu, Xuan Lu, Xin Rahman, Mati Ur She, Zi-Hang Shanghai Univ Dept Math Shanghai 200444 Peoples R China Shanghai Jiao Tong Univ Sch Math Sci Shanghai 200240 Peoples R China Foshan Univ Sch Math & Big Data Foshan 528000 Peoples R China Hanshan Normal Univ Dept Math Chaozhou 521041 Peoples R China

In this article, neural network method (NNM) is presented to solve the spatiotemporal variable-order fractional advection-diffusion equation with a nonlinear source term. The network is established by using shifted Legendre orthogonal polynomials with adjustable coefficients. According to the properties of variable fractional derivative, the loss function of neural network is deduced theoretically. Assume that the source function satisfies the Lipschitz hypothesis, the reasonable range for learning rate is discussed in details. Then neural networks are trained repeatedly on the training set to reduce the loss functions for two numerical examples. Numerical results show that the neural network method is better than the finite difference method in solving some nonlinear variable fractional order problems. Finally, several graphs and some numerical analysis are given to confirm our conclusions.(c) 2022 Elsevier Ltd. All rights reserved.

关键词： Variable-order fractional derivative neural network method Fractional advection-diffusion equation

来源：评论

学校读者我要写书评

暂无评论

Study of fractional-order reaction-advection-diffusion equation using neural network method

引用

MATHEMATICS AND COMPUTERS IN SIMULATION 2023年第1期208卷 15-27页

作者： Biswas, Chetna Singh, Anup Chopra, Manish Das, Subir Indian Inst Technol BHU Dept Math Sci Varanasi 221005 Uttar Pradesh India Nirma Univ Inst Technol Dept Math Ahmadabad 382481 Gujarat India Bhabha Atom Res Ctr Radiat Safety Syst Div Mumbai 400085 Maharashtra India

In the present article the spatio-temporal fractional-order nonlinear reaction-advection-diffusion equation is solved using the neural network method (NNM). Shifted Legendre orthogonal polynomials with variable coefficients are used in the network's construction. The characteristics of a fractional-order derivative are used to determine the loss function of a neural network. The permissible learning rate range is discussed in detail, assuming that the Lipschitz hypothesis is accurate for the nonlinearity in reaction term. We have demonstrated the application of the NNM on two numerical examples by utilizing the neural networks which had been repeatedly trained on the training set. In other words, we have validated the effectiveness of the method for such problems. The effects of reaction term and also the degree of nonlinearity in reaction and advection terms on the solution profile are visualized through graphical presentations for specific test cases. (c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

关键词： Fractional-order reaction-advection-diffusion equation neural network method Artificial neural network loss function Damping

来源：评论

学校读者我要写书评

暂无评论

A broadband low-frequency muffler based on neural network method and Helmholtz resonator with helical neck

引用

JOURNAL OF VIBRATION AND CONTROL 2023年第17-18期29卷 3942-3951页

作者： Bai, Chungeng Wu, Fengmin Wang, Junjun Jiang, Jiuxing Yang, Bin Harbin Univ Sci & Technol Sch Sci Dept Phys Harbin 150080 Heilongjiang Peoples R China Harbin Inst Technol Sch Instrumentat Sci & Engn Funct Mat & Acousto Opt Instruments Inst Harbin Peoples R China

In this study, a design method of broadband low-frequency muffler based on NN method and Helmholtz resonators with helical necks is proposed, which ensures almost perfect ventilation and broadband sound insulation in the low- and medium-frequency range. First, the sound insulation performance of the muffler is improved by adding a helical structure at the port. The slit Helmholtz resonator with a helical structure is able to reduce the cross-sectional area of the resonator port and increase the contact area of thermal viscosity loss, thus reducing the peak frequency of sound insulation and increasing the sound energy loss. Using finite element analysis software, the structural transmission loss is simulated. At the same time, the neural network method is used to predict the combined structure, then, the combined structure can be designed quickly and reasonably to achieve the sound insulation of medium- and low-frequency broadband. Experimental and simulation results show that in the target range of 430 Hz-2220 Hz, the overall TL exceeds 30 dB and the maximum exceeds 60 dB. In addition, when a helical structure is added, the overall pipeline remains unchanged;and when a muffler is added on the basis, the perfect ventilation effect can be achieved. The proposed structural model and the idea of rapid design lay a great foundation for the design and optimization of broadband muffler.

关键词： Helmholtz resonator broadband low-frequency muffler neural network method

来源：评论

学校读者我要写书评

暂无评论

Brittleness assessment of the shale oil reservoir based on neural network method: A case study of the Yanchang Formation, Ordos Basin

引用

UNCONVENTIONAL RESOURCES 2023年第1期3卷 54-60页

作者： Ju, Wei Liang, Yan Feng, Shengbin Xin, Honggang You, Yuan Ning, Weike Yu, Guodong China Univ Min & Technol Sch Resources & Geosci Xuzhou 221116 Jiangsu Peoples R China PetroChina Changqing Oilfield Co Inst Explorat & Dev Xian 710018 Shaanxi Peoples R China

The Chang 7 oil-bearing layer of Yanchang Formation is rich in shale oil resources. However, the reservoir indicates strong reservoir heterogeneity and has obvious differences in productivity among wells. The brittleness acts as an important factor causing the above phenomenon. Studies on rock mechanical properties and brittleness evaluation can provide technical support for drilling and fracturing design, but current methods have many disadvantages such as difficulty in obtaining parameters. In this study, the neural network method is used to construct the relationship between elastic modulus, Poisson's ratio and logging curve on the basis of measured rock mechanical parameters, construct rock mechanics parameter profile in the whole well section of Chang 7 oil-bearing layer, and finally quantitative evaluate shale oil reservoir brittleness. The results indicate that, (1) the neural network method is an effective method for rock mechanical parameter prediction and brittleness evaluation. The error between the predicted and measured values of elastic modulus and Poisson's ratio is low, generally within 10%;(2) according to the brittleness evaluation results, on the whole, the brittleness index of the Chang 7(2) reservoir is high, and the brittleness index of the Chang 7(3) reservoir is low. The results can provide scientific guidance for benefit development of Chang 7 shale oil in the Ordos Basin.

关键词： Brittleness Shale oil neural network method Yanchang Formation Ordos Basin

来源：评论

学校读者我要写书评

暂无评论

neural network method for fractional-order partial differential equations

引用

NEUROCOMPUTING 2020年 414卷 225-237页

作者： Qu, Haidong Liu, Xuan She, Zihang Hanshan Normal Univ Dept Math Chaozhou 521041 Peoples R China

In this paper, neural network method is first proposed to solve the fractional-order partial differential equations. The neural network based on the sine and the cosine functions is established on the sample points which are evenly distributed in the solution area. In view of the fractional heat conduction equation and the fractional wave equation, the training error function is established, and the related algorithm for the initial boundary value problem of the above equations is given. Then, the learning rate of the neural network is analyzed. Finally, several numerical examples are given to verify the effectiveness of solving the fractional-order partial differential equations by the present method. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Fractional partial differential equations neural network method Fractional heat conduction equation Fractional wave equation

来源：评论

学校读者我要写书评

暂无评论

neural network method for solving fractional diffusion equations

引用

APPLIED MATHEMATICS AND COMPUTATION 2021年 391卷 125635-125635页

作者： Qu, Haidong She, Zihang Liu, Xuan Hanshan Normal Univ Dept Math Chaozhou 515041 Peoples R China

In this paper, neural networks based on Legendre polynomials are established to solve space and time fractional diffusion equations. The error functions containing adjustable parameters (the weights) for the training sets are constructed. The range of learning rate is analyzed to ensure that the error decreases with respect to training times. Several nu-merical examples including numerical results and graphs are illustrated. The results show that more training can achieve high precision. (c) 2020 Elsevier Inc. All rights reserved.

关键词： Fractional diffusion equation neural network method Time fractional derivative Space fractional derivative Time-space fractional derivative

来源：评论

学校读者我要写书评

暂无评论

Researching the Link Between the Geometric and Renyi Discord for Special Canonical Initial States Based on neural network method

引用

CMC-COMPUTERS MATERIALS & CONTINUA 2019年第3期60卷 1087-1095页

作者： Li, Xiaoyu Zhu, Qinsheng Meng, Qingyu You, Caishu Zhu, Mingzheng Hu, Yong Huang, Yiming Wu, Hao Zheng, Desheng Univ Elect Sci & Technol China Sch Informat & Software Engn Chengdu 610054 Peoples R China Univ Elect Sci & Technol China Sch Phys Chengdu 610054 Peoples R China Univ Maryland Inst Adv Comp Studies Washington DC USA Southwest Petr Univ Sch Comp Sci Chengdu 61050 Peoples R China

Quantum correlation which is different to the entanglement and classical correlation plays important role in quantum information field. In our setup, neural network method is adopted to simulate the link between the Renyi discord (alpha = 2) and the geometric discord (Bures distance) for special canonical initial states in order to show the consistency of physical results for different quantification methods. Our results are useful for studying the differences and commonalities of different quantizing methods of quantum correlation.

关键词： neural network method quantum correlation renyi discord geometric discord

来源：评论

学校读者我要写书评

暂无评论

Efficient SLW models for water vapor and carbon dioxide based on neural network method

引用

JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER 2019年 236卷 106600-106600页

作者： Sun, Yujia Ma, Jiajia Yu, Ying Ye, Bin Gao, Cai Hefei Univ Technol Sch Automot & Transportat Engn Hefei 230009 Anhui Peoples R China Northwest Inst Mech & Elect Engn Xianyang 712009 Shanxi Peoples R China China Acad Launch Vehicle Technol Sci & Technol Space Phys Lab Beijing 100076 Peoples R China

Non-gray gas radiation plays an important role in combustion system, and the spectral-line-based weighted-sum-of-gray-gases (SLW) is a popular model to treat the gas radiative properties. In practical applications, the inverse calculations of the cross-sections from a specified F are time demanding. The neural network method is used here to develop inverse absorption line blackbody distribution function (ALBDF) to efficiently and accurately calculate the cross-sections from F. Results show that the neural network based SLW can predict the inverse ALBDF very well and the relative errors for the radiative heat source and heat flux for the radiation transfer are less than 2%. The computational time of the neural network based SLW is only 1/10th of the original SLW model. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Gas radiation SLW method neural network method

来源：评论

学校读者我要写书评

暂无评论

Short-Term Harmonic Forecasting and Evaluation Affected by Electrified Railways on the Power Grid Based on Stack Auto Encoder neural network method and the Comparison to BP method 13

Short-Term Harmonic Forecasting and Evaluation Affected by E...

引用

13th IEEE Conference on Industrial Electronics and Applications (ICIEA)

作者： Pang, Yan Li, Haoguang China Univ Petr Shengli Coll Dongying Peoples R China

ISBN: (纸本)9781538637586

With the development towards high-speed, highcapacity, high-density networking of high-speed railway, harmonic problems caused by high-speed locomotives are getting more and more serious, which has been a great threaten to the safety and stability of power system operation. The way of evaluation on the influence of railway becomes increasingly important. The method of short-term harmonic forecasting and evaluation affected by electrified railways on the power grid based on Stack Auto Encoder (SAE) neural network model and based on BP method are proposed respectively in this study. At first, this paper makes an introduction and analysis on the methods of harmonic evaluation affected by electrified railways on the power grid, and the importance of short-term harmonic forecasting and evaluation affected by electrified railways on the power grid was emphasized. Then, it makes an analysis on the theory of short-term harmonic forecasting affected by electrified railways on the power grid based on Stack Auto Encoder neural network model and based on BP model respectively, and the two kind of method of evaluation on harmonic evaluation are introduced. Then, the model and method of short-term harmonic forecasting and evaluation affected by electrified railways on the power grid based on Stack Auto Encoder neural network method and based on BP method are proposed respectively, which are used in the case. Besides, the results of harmonic forecasting achieves the purpose of the harmonic forecasting, and the harmonic value is evaluated using the ways of harmonic evaluation. On one hand, it proves the Stack Auto Encoder neural network method is prior to the on BP method on harmonic forecasting affected by electrified railways on the power grid. It provides a theoretical reference for the harmonic evaluation on the influence of railway, which can also make an improvement of the power quality in power network.

关键词： short-term harmonic forecasting Stack Auto Encoder neural network method harmonic evaluation electrified railways power grid

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：