{"title":"通过重叠改进节点选择以解决椭圆问题的无监督[公式省略]均值机器学习算法","authors":"","doi":"10.1016/j.enganabound.2024.105919","DOIUrl":null,"url":null,"abstract":"<div><p>We propose an overlapping algorithm utilizing the <span><math><mi>K</mi></math></span>-means clustering technique to group scattered data nodes for discretizing elliptic partial differential equations. Unlike conventional kernel-based approximation methods, which select the closest points from the entire region for each center, our algorithm selects only the nearest points within each overlapping cluster. We present computational results to demonstrate the efficiency of our algorithm for both two-dimensional and three-dimensional problems. For evaluation and validation, these results are compared with results obtained using the RBF-FD+polynomial method with different kernels.</p></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":null,"pages":null},"PeriodicalIF":4.2000,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An unsupervised K-means machine learning algorithm via overlapping to improve the nodes selection for solving elliptic problems\",\"authors\":\"\",\"doi\":\"10.1016/j.enganabound.2024.105919\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We propose an overlapping algorithm utilizing the <span><math><mi>K</mi></math></span>-means clustering technique to group scattered data nodes for discretizing elliptic partial differential equations. Unlike conventional kernel-based approximation methods, which select the closest points from the entire region for each center, our algorithm selects only the nearest points within each overlapping cluster. We present computational results to demonstrate the efficiency of our algorithm for both two-dimensional and three-dimensional problems. For evaluation and validation, these results are compared with results obtained using the RBF-FD+polynomial method with different kernels.</p></div>\",\"PeriodicalId\":51039,\"journal\":{\"name\":\"Engineering Analysis with Boundary Elements\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.2000,\"publicationDate\":\"2024-08-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Engineering Analysis with Boundary Elements\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S095579972400393X\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Engineering Analysis with Boundary Elements","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S095579972400393X","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
An unsupervised K-means machine learning algorithm via overlapping to improve the nodes selection for solving elliptic problems
We propose an overlapping algorithm utilizing the -means clustering technique to group scattered data nodes for discretizing elliptic partial differential equations. Unlike conventional kernel-based approximation methods, which select the closest points from the entire region for each center, our algorithm selects only the nearest points within each overlapping cluster. We present computational results to demonstrate the efficiency of our algorithm for both two-dimensional and three-dimensional problems. For evaluation and validation, these results are compared with results obtained using the RBF-FD+polynomial method with different kernels.
期刊介绍:
This journal is specifically dedicated to the dissemination of the latest developments of new engineering analysis techniques using boundary elements and other mesh reduction methods.
Boundary element (BEM) and mesh reduction methods (MRM) are very active areas of research with the techniques being applied to solve increasingly complex problems. The journal stresses the importance of these applications as well as their computational aspects, reliability and robustness.
The main criteria for publication will be the originality of the work being reported, its potential usefulness and applications of the methods to new fields.
In addition to regular issues, the journal publishes a series of special issues dealing with specific areas of current research.
The journal has, for many years, provided a channel of communication between academics and industrial researchers working in mesh reduction methods
Fields Covered:
• Boundary Element Methods (BEM)
• Mesh Reduction Methods (MRM)
• Meshless Methods
• Integral Equations
• Applications of BEM/MRM in Engineering
• Numerical Methods related to BEM/MRM
• Computational Techniques
• Combination of Different Methods
• Advanced Formulations.