{"title":"深度学习驱动的领域分解(DLD3):结构分析的通用人工智能驱动框架","authors":"","doi":"10.1016/j.cma.2024.117446","DOIUrl":null,"url":null,"abstract":"<div><div>A novel, generalizable Artificial Intelligence (AI)-driven technique, termed Deep Learning-Driven Domain Decomposition (DLD<span><math><msup><mrow></mrow><mrow><mn>3</mn></mrow></msup></math></span>), is introduced for simulating two-dimensional linear elasticity problems with arbitrary geometries and boundary conditions (BCs). The DLD<span><math><msup><mrow></mrow><mrow><mn>3</mn></mrow></msup></math></span> framework leverages trained AI models to predict the displacement field within small subdomains, each characterized by varying geometries and BCs. To enforce continuity across the entire domain, the overlapping Schwarz domain decomposition method (DDM) iteratively updates the BCs of each subdomain, thus approximating the overall solution. After evaluating multiple model architectures, the Fourier Neural Operator (FNO) was selected as the AI engine for the DLD<span><math><msup><mrow></mrow><mrow><mn>3</mn></mrow></msup></math></span> method, owing to its data efficiency and high accuracy. We also present a framework that utilizes geometry reconstruction and automated meshing algorithms to generate millions of training data points from high-fidelity finite element (FE) simulations. Several case studies are provided to demonstrate the DLD<span><math><msup><mrow></mrow><mrow><mn>3</mn></mrow></msup></math></span> algorithm’s ability to accurately predict displacement fields in problems involving complex geometries, diverse BCs, and material properties.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9000,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Deep learning-driven domain decomposition (DLD3): A generalizable AI-driven framework for structural analysis\",\"authors\":\"\",\"doi\":\"10.1016/j.cma.2024.117446\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>A novel, generalizable Artificial Intelligence (AI)-driven technique, termed Deep Learning-Driven Domain Decomposition (DLD<span><math><msup><mrow></mrow><mrow><mn>3</mn></mrow></msup></math></span>), is introduced for simulating two-dimensional linear elasticity problems with arbitrary geometries and boundary conditions (BCs). The DLD<span><math><msup><mrow></mrow><mrow><mn>3</mn></mrow></msup></math></span> framework leverages trained AI models to predict the displacement field within small subdomains, each characterized by varying geometries and BCs. To enforce continuity across the entire domain, the overlapping Schwarz domain decomposition method (DDM) iteratively updates the BCs of each subdomain, thus approximating the overall solution. After evaluating multiple model architectures, the Fourier Neural Operator (FNO) was selected as the AI engine for the DLD<span><math><msup><mrow></mrow><mrow><mn>3</mn></mrow></msup></math></span> method, owing to its data efficiency and high accuracy. We also present a framework that utilizes geometry reconstruction and automated meshing algorithms to generate millions of training data points from high-fidelity finite element (FE) simulations. Several case studies are provided to demonstrate the DLD<span><math><msup><mrow></mrow><mrow><mn>3</mn></mrow></msup></math></span> algorithm’s ability to accurately predict displacement fields in problems involving complex geometries, diverse BCs, and material properties.</div></div>\",\"PeriodicalId\":55222,\"journal\":{\"name\":\"Computer Methods in Applied Mechanics and Engineering\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":6.9000,\"publicationDate\":\"2024-10-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computer Methods in Applied Mechanics and Engineering\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0045782524007011\",\"RegionNum\":1,\"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":"Computer Methods in Applied Mechanics and Engineering","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0045782524007011","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
摘要
本文介绍了一种新颖的、可推广的人工智能(AI)驱动技术,称为深度学习驱动的领域分解(DLD3),用于模拟具有任意几何形状和边界条件(BC)的二维线性弹性问题。DLD3 框架利用训练有素的人工智能模型来预测小型子域内的位移场,每个子域的几何形状和边界条件各不相同。为了确保整个域的连续性,重叠施瓦茨域分解法(DDM)会迭代更新每个子域的边界条件,从而逼近整体解决方案。在对多种模型架构进行评估后,我们选择了傅立叶神经运算器(FNO)作为 DLD3 方法的人工智能引擎,因为它具有数据效率高、精度高的特点。我们还介绍了一个框架,该框架利用几何重构和自动网格划分算法,从高保真有限元(FE)模拟中生成数百万个训练数据点。我们提供了几个案例研究,以证明 DLD3 算法在涉及复杂几何形状、不同 BC 和材料属性的问题中准确预测位移场的能力。
Deep learning-driven domain decomposition (DLD3): A generalizable AI-driven framework for structural analysis
A novel, generalizable Artificial Intelligence (AI)-driven technique, termed Deep Learning-Driven Domain Decomposition (DLD), is introduced for simulating two-dimensional linear elasticity problems with arbitrary geometries and boundary conditions (BCs). The DLD framework leverages trained AI models to predict the displacement field within small subdomains, each characterized by varying geometries and BCs. To enforce continuity across the entire domain, the overlapping Schwarz domain decomposition method (DDM) iteratively updates the BCs of each subdomain, thus approximating the overall solution. After evaluating multiple model architectures, the Fourier Neural Operator (FNO) was selected as the AI engine for the DLD method, owing to its data efficiency and high accuracy. We also present a framework that utilizes geometry reconstruction and automated meshing algorithms to generate millions of training data points from high-fidelity finite element (FE) simulations. Several case studies are provided to demonstrate the DLD algorithm’s ability to accurately predict displacement fields in problems involving complex geometries, diverse BCs, and material properties.
期刊介绍:
Computer Methods in Applied Mechanics and Engineering stands as a cornerstone in the realm of computational science and engineering. With a history spanning over five decades, the journal has been a key platform for disseminating papers on advanced mathematical modeling and numerical solutions. Interdisciplinary in nature, these contributions encompass mechanics, mathematics, computer science, and various scientific disciplines. The journal welcomes a broad range of computational methods addressing the simulation, analysis, and design of complex physical problems, making it a vital resource for researchers in the field.