{"title":"Multilayer Neural Networks Enhanced With Hybrid Methods for Solving Fractional Partial Differential Equations","authors":"Amina Hassan Ali, Norazak Senu, Ali Ahmadian","doi":"10.1002/jnm.70073","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>This paper introduces a novel multilayer neural network technique to solve partial differential equations with non-integer derivatives (FPDEs). The proposed model is a deep feed-forward multiple layer neural network (DFMLNN) that is trained using advanced optimization approaches, namely adaptive moment estimation (Adam) and limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS), which integrate neural networks. First, the Adam method is employed for training, and then the model is further improved using L-BFGS. The Laplace transform is used, concentrating on the Caputo fractional derivative, to approximate the FPDE. The efficacy of this strategy is confirmed through rigorous testing, which involves making predictions and comparing the outcomes with exact solutions. The results illustrate that this combined approach greatly improves both precision and effectiveness. This proposed multilayer neural network offers a robust and reliable framework for solving FPDEs.</p>\n </div>","PeriodicalId":50300,"journal":{"name":"International Journal of Numerical Modelling-Electronic Networks Devices and Fields","volume":"38 4","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Numerical Modelling-Electronic Networks Devices and Fields","FirstCategoryId":"5","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/jnm.70073","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0
Abstract
This paper introduces a novel multilayer neural network technique to solve partial differential equations with non-integer derivatives (FPDEs). The proposed model is a deep feed-forward multiple layer neural network (DFMLNN) that is trained using advanced optimization approaches, namely adaptive moment estimation (Adam) and limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS), which integrate neural networks. First, the Adam method is employed for training, and then the model is further improved using L-BFGS. The Laplace transform is used, concentrating on the Caputo fractional derivative, to approximate the FPDE. The efficacy of this strategy is confirmed through rigorous testing, which involves making predictions and comparing the outcomes with exact solutions. The results illustrate that this combined approach greatly improves both precision and effectiveness. This proposed multilayer neural network offers a robust and reliable framework for solving FPDEs.
期刊介绍:
Prediction through modelling forms the basis of engineering design. The computational power at the fingertips of the professional engineer is increasing enormously and techniques for computer simulation are changing rapidly. Engineers need models which relate to their design area and which are adaptable to new design concepts. They also need efficient and friendly ways of presenting, viewing and transmitting the data associated with their models.
The International Journal of Numerical Modelling: Electronic Networks, Devices and Fields provides a communication vehicle for numerical modelling methods and data preparation methods associated with electrical and electronic circuits and fields. It concentrates on numerical modelling rather than abstract numerical mathematics.
Contributions on numerical modelling will cover the entire subject of electrical and electronic engineering. They will range from electrical distribution networks to integrated circuits on VLSI design, and from static electric and magnetic fields through microwaves to optical design. They will also include the use of electrical networks as a modelling medium.