Lin Qiu, Fajie Wang, Wenzhen Qu, Yan Gu, Qing-Hua Qin
{"title":"Spectral integrated neural networks (SINNs) for solving forward and inverse dynamic problems.","authors":"Lin Qiu, Fajie Wang, Wenzhen Qu, Yan Gu, Qing-Hua Qin","doi":"10.1016/j.neunet.2024.106756","DOIUrl":null,"url":null,"abstract":"<p><p>This study introduces an innovative neural network framework named spectral integrated neural networks (SINNs) to address both forward and inverse dynamic problems in three-dimensional space. In the SINNs, the spectral integration technique is utilized for temporal discretization, followed by the application of a fully connected neural network to solve the resulting partial differential equations in the spatial domain. Furthermore, the polynomial basis functions are employed to expand the unknown function, with the goal of improving the performance of SINNs in tackling inverse problems. The performance of the developed framework is evaluated through several dynamic benchmark examples encompassing linear and nonlinear heat conduction problems, linear and nonlinear wave propagation problems, inverse problem of heat conduction, and long-time heat conduction problem. The numerical results demonstrate that the SINNs can effectively and accurately solve forward and inverse problems involving heat conduction and wave propagation. Additionally, the SINNs provide precise and stable solutions for dynamic problems with extended time durations. Compared to commonly used physics-informed neural networks, the SINNs exhibit superior performance with enhanced convergence speed, computational accuracy, and efficiency.</p>","PeriodicalId":49763,"journal":{"name":"Neural Networks","volume":null,"pages":null},"PeriodicalIF":6.0000,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Neural Networks","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1016/j.neunet.2024.106756","RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/9/22 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
Abstract
This study introduces an innovative neural network framework named spectral integrated neural networks (SINNs) to address both forward and inverse dynamic problems in three-dimensional space. In the SINNs, the spectral integration technique is utilized for temporal discretization, followed by the application of a fully connected neural network to solve the resulting partial differential equations in the spatial domain. Furthermore, the polynomial basis functions are employed to expand the unknown function, with the goal of improving the performance of SINNs in tackling inverse problems. The performance of the developed framework is evaluated through several dynamic benchmark examples encompassing linear and nonlinear heat conduction problems, linear and nonlinear wave propagation problems, inverse problem of heat conduction, and long-time heat conduction problem. The numerical results demonstrate that the SINNs can effectively and accurately solve forward and inverse problems involving heat conduction and wave propagation. Additionally, the SINNs provide precise and stable solutions for dynamic problems with extended time durations. Compared to commonly used physics-informed neural networks, the SINNs exhibit superior performance with enhanced convergence speed, computational accuracy, and efficiency.
期刊介绍:
Neural Networks is a platform that aims to foster an international community of scholars and practitioners interested in neural networks, deep learning, and other approaches to artificial intelligence and machine learning. Our journal invites submissions covering various aspects of neural networks research, from computational neuroscience and cognitive modeling to mathematical analyses and engineering applications. By providing a forum for interdisciplinary discussions between biology and technology, we aim to encourage the development of biologically-inspired artificial intelligence.