Multilayer Neural Networks Enhanced With Hybrid Methods for Solving Fractional Partial Differential Equations

IF 1.6 4区 工程技术 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC
Amina Hassan Ali, Norazak Senu, Ali Ahmadian
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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.

用混合方法增强多层神经网络求解分数阶偏微分方程
介绍了一种求解非整数导数偏微分方程的多层神经网络技术。所提出的模型是一个深度前馈多层神经网络(DFMLNN),使用先进的优化方法进行训练,即自适应矩估计(Adam)和有限记忆Broyden-Fletcher-Goldfarb-Shanno (L-BFGS),这两种方法集成了神经网络。首先使用Adam方法进行训练,然后使用L-BFGS进一步改进模型。使用拉普拉斯变换,集中于卡普托分数阶导数,来近似FPDE。这种策略的有效性是通过严格的测试来证实的,测试包括做出预测,并将结果与精确的解决方案进行比较。结果表明,这种组合方法大大提高了精度和有效性。所提出的多层神经网络为求解fpga提供了一个鲁棒可靠的框架。
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来源期刊
CiteScore
4.60
自引率
6.20%
发文量
101
审稿时长
>12 weeks
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.
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