Intelligent predictive computing for functional differential system in quantum calculus

3区 计算机科学 Q1 Computer Science Journal of Ambient Intelligence and Humanized Computing Pub Date : 2024-03-22 DOI:10.1007/s12652-023-04744-0
Syed Ali Asghar, Hira Ilyas, Shafaq Naz, Muhammad Asif Zahoor Raja, Iftikhar Ahmad, Muhammad Shaoib
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Abstract

The aim of this study is to present a novel application of Levenberg–Marquardt backpropagation (LMB) to investigate numerically the solution of functional differential equations (FDE) arising in quantum calculus models (QCMs). The various types of discrete versions of FDM in QCMs are always found to be stiff to solve due to involvement of delay and to overcome the said difficulty, we proposed intelligent computing platform via LMB networks. In order to generate dataset for LMB networks, firstly, the FDEs in QCMs are converted into recurrence relations, then these recurrence systems are solved numerically on a specific input grids in case of both types of FDEs with q-exponential function as well as stable with decreasing behavior characteristics. The training, testing and validation samples based processes are employed to construct LMB networks by exploiting approximation theory on mean square error sense for obtaining the solutions of both types of FDEs. The exhaustive conducted simulation studies for solving FDEs in QCMs via absolute error and mean squared error endorse the accuracy, potential, convergence, stability and worth of proposed technique, which further certified through viable training state parameters, outcomes of error histograms, values of regression/correlation indices.

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量子微积分中函数微分系统的智能预测计算
本研究的目的是提出一种莱文伯格-马夸特反向传播(LMB)的新应用,以数值研究量子微积分模型(QCM)中出现的函数微分方程(FDE)的解法。量子微积分模型中的各类离散型 FDM 总是因涉及延迟而难以求解,为了克服上述困难,我们提出了通过 LMB 网络的智能计算平台。为了生成 LMB 网络的数据集,首先将 QCM 中的 FDE 转换为递推关系,然后在特定输入网格上对具有 q 指数函数和稳定递减行为特征的两类 FDE 进行数值求解。通过利用均方误差意义上的近似理论,采用基于训练、测试和验证样本的过程来构建 LMB 网络,从而获得两类 FDE 的解。通过绝对误差和均方误差对求解 QCM 中的 FDE 进行了详尽的模拟研究,证明了所提技术的准确性、潜力、收敛性、稳定性和价值,并通过可行的训练状态参数、误差直方图结果、回归/相关指数值进一步证实了这一点。
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来源期刊
Journal of Ambient Intelligence and Humanized Computing
Journal of Ambient Intelligence and Humanized Computing COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCEC-COMPUTER SCIENCE, INFORMATION SYSTEMS
CiteScore
9.60
自引率
0.00%
发文量
854
期刊介绍: The purpose of JAIHC is to provide a high profile, leading edge forum for academics, industrial professionals, educators and policy makers involved in the field to contribute, to disseminate the most innovative researches and developments of all aspects of ambient intelligence and humanized computing, such as intelligent/smart objects, environments/spaces, and systems. The journal discusses various technical, safety, personal, social, physical, political, artistic and economic issues. The research topics covered by the journal are (but not limited to): Pervasive/Ubiquitous Computing and Applications Cognitive wireless sensor network Embedded Systems and Software Mobile Computing and Wireless Communications Next Generation Multimedia Systems Security, Privacy and Trust Service and Semantic Computing Advanced Networking Architectures Dependable, Reliable and Autonomic Computing Embedded Smart Agents Context awareness, social sensing and inference Multi modal interaction design Ergonomics and product prototyping Intelligent and self-organizing transportation networks & services Healthcare Systems Virtual Humans & Virtual Worlds Wearables sensors and actuators
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