{"title":"奇异扰动边界值问题的半解析 PINN 方法","authors":"Gung-Min Gie, Youngjoon Hong, Chang-Yeol Jung","doi":"10.1080/00036811.2024.2302405","DOIUrl":null,"url":null,"abstract":"In this paper, we propose a novel semi-analytic physics informed neural network (PINN) method for solving singularly perturbed boundary value problems. The PINN is a scientific machine learning fra...","PeriodicalId":55507,"journal":{"name":"Applicable Analysis","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Semi-analytic PINN methods for singularly perturbed boundary value problems\",\"authors\":\"Gung-Min Gie, Youngjoon Hong, Chang-Yeol Jung\",\"doi\":\"10.1080/00036811.2024.2302405\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we propose a novel semi-analytic physics informed neural network (PINN) method for solving singularly perturbed boundary value problems. The PINN is a scientific machine learning fra...\",\"PeriodicalId\":55507,\"journal\":{\"name\":\"Applicable Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2024-01-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applicable Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1080/00036811.2024.2302405\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applicable Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/00036811.2024.2302405","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Semi-analytic PINN methods for singularly perturbed boundary value problems
In this paper, we propose a novel semi-analytic physics informed neural network (PINN) method for solving singularly perturbed boundary value problems. The PINN is a scientific machine learning fra...
期刊介绍：
Applicable Analysis is concerned primarily with analysis that has application to scientific and engineering problems. Papers should indicate clearly an application of the mathematics involved. On the other hand, papers that are primarily concerned with modeling rather than analysis are outside the scope of the journal
General areas of analysis that are welcomed contain the areas of differential equations, with emphasis on PDEs, and integral equations, nonlinear analysis, applied functional analysis, theoretical numerical analysis and approximation theory. Areas of application, for instance, include the use of homogenization theory for electromagnetic phenomena, acoustic vibrations and other problems with multiple space and time scales, inverse problems for medical imaging and geophysics, variational methods for moving boundary problems, convex analysis for theoretical mechanics and analytical methods for spatial bio-mathematical models.
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