Jiale Linghu , Weifeng Gao , Hao Dong , Yufeng Nie , Shuqi Wang
{"title":"复合材料准静态热力学问题的高阶多尺度神经网络方法","authors":"Jiale Linghu , Weifeng Gao , Hao Dong , Yufeng Nie , Shuqi Wang","doi":"10.1016/j.apm.2025.116232","DOIUrl":null,"url":null,"abstract":"<div><div>The high-accuracy simulation of multi-physics and multi-scale problems of composite materials with a neural network approach remains a challenging task due to costly computation and Frequency Principle. In this study, a novel high-order multi-scale neural network approach with high-accuracy and efficiency performance is developed to compute the quasi-static thermo-mechanical problems of composite materials, which combines the computational advantages of the high-order multi-scale method and the neural network-based method. In the computational framework of high-order multi-scale neural network, the high-order multi-scale method decomposes the original complex multi-scale problem into two parts, namely, the macroscopic homogenized problem and the microscopic unit cell problems. Then the neural network method mesh-free computes these two parts. In particular, revised physics-informed neural networks are developed to calculate macroscopic homogenized thermo-mechanical problems with significant order of magnitude differences between different physical fields. Finally, the accuracy and efficiency of the proposed high-order multi-scale neural network method are demonstrated by representative numerical examples of two- and three-dimensional simulations of composite materials.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"148 ","pages":"Article 116232"},"PeriodicalIF":4.4000,"publicationDate":"2025-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"High-order multi-scale neural network method for quasi-static thermo-mechanical problems of composite materials\",\"authors\":\"Jiale Linghu , Weifeng Gao , Hao Dong , Yufeng Nie , Shuqi Wang\",\"doi\":\"10.1016/j.apm.2025.116232\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>The high-accuracy simulation of multi-physics and multi-scale problems of composite materials with a neural network approach remains a challenging task due to costly computation and Frequency Principle. In this study, a novel high-order multi-scale neural network approach with high-accuracy and efficiency performance is developed to compute the quasi-static thermo-mechanical problems of composite materials, which combines the computational advantages of the high-order multi-scale method and the neural network-based method. In the computational framework of high-order multi-scale neural network, the high-order multi-scale method decomposes the original complex multi-scale problem into two parts, namely, the macroscopic homogenized problem and the microscopic unit cell problems. Then the neural network method mesh-free computes these two parts. In particular, revised physics-informed neural networks are developed to calculate macroscopic homogenized thermo-mechanical problems with significant order of magnitude differences between different physical fields. Finally, the accuracy and efficiency of the proposed high-order multi-scale neural network method are demonstrated by representative numerical examples of two- and three-dimensional simulations of composite materials.</div></div>\",\"PeriodicalId\":50980,\"journal\":{\"name\":\"Applied Mathematical Modelling\",\"volume\":\"148 \",\"pages\":\"Article 116232\"},\"PeriodicalIF\":4.4000,\"publicationDate\":\"2025-06-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematical Modelling\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0307904X25003075\",\"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":"Applied Mathematical Modelling","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0307904X25003075","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}
High-order multi-scale neural network method for quasi-static thermo-mechanical problems of composite materials
The high-accuracy simulation of multi-physics and multi-scale problems of composite materials with a neural network approach remains a challenging task due to costly computation and Frequency Principle. In this study, a novel high-order multi-scale neural network approach with high-accuracy and efficiency performance is developed to compute the quasi-static thermo-mechanical problems of composite materials, which combines the computational advantages of the high-order multi-scale method and the neural network-based method. In the computational framework of high-order multi-scale neural network, the high-order multi-scale method decomposes the original complex multi-scale problem into two parts, namely, the macroscopic homogenized problem and the microscopic unit cell problems. Then the neural network method mesh-free computes these two parts. In particular, revised physics-informed neural networks are developed to calculate macroscopic homogenized thermo-mechanical problems with significant order of magnitude differences between different physical fields. Finally, the accuracy and efficiency of the proposed high-order multi-scale neural network method are demonstrated by representative numerical examples of two- and three-dimensional simulations of composite materials.
期刊介绍:
Applied Mathematical Modelling focuses on research related to the mathematical modelling of engineering and environmental processes, manufacturing, and industrial systems. A significant emerging area of research activity involves multiphysics processes, and contributions in this area are particularly encouraged.
This influential publication covers a wide spectrum of subjects including heat transfer, fluid mechanics, CFD, and transport phenomena; solid mechanics and mechanics of metals; electromagnets and MHD; reliability modelling and system optimization; finite volume, finite element, and boundary element procedures; modelling of inventory, industrial, manufacturing and logistics systems for viable decision making; civil engineering systems and structures; mineral and energy resources; relevant software engineering issues associated with CAD and CAE; and materials and metallurgical engineering.
Applied Mathematical Modelling is primarily interested in papers developing increased insights into real-world problems through novel mathematical modelling, novel applications or a combination of these. Papers employing existing numerical techniques must demonstrate sufficient novelty in the solution of practical problems. Papers on fuzzy logic in decision-making or purely financial mathematics are normally not considered. Research on fractional differential equations, bifurcation, and numerical methods needs to include practical examples. Population dynamics must solve realistic scenarios. Papers in the area of logistics and business modelling should demonstrate meaningful managerial insight. Submissions with no real-world application will not be considered.