基于Legendre的神经网络与启发式算法集成,用于分析洛伦茨混乱模型:一个智能和比较研究
Khalid Masood1, Muhammad Arshad2, Muhammad Abubakar3
1Department of Computer Science, Lahore Garrison University, Lahore, Pakistan. kmasoodk@gmail.com.
Scientific reports
|April 24, 2025
概括
使用Legendre多项式人工神经网络 (LENN) 的智能计算框架,并使用Firefly (FA) 和阿基米德优化算法 (AOA) 进行优化,有效地管理洛伦兹模型. 这种LENN-FA-AOA方法最大限度地降低了解决高精度非线性混乱系统的计算成本.
科学领域:
- 计算数学 计算数学 计算数学
- 人工智能的人工智能
- 混沌理论 混沌理论
背景情况:
- 洛伦茨模型是混沌理论中的一个基本系统,由于其混乱的性质,它对数值解决方案提出了重大挑战.
- 解决非线性混乱系统的传统方法可能是计算密集的,可能缺乏稳定性.
- 智能计算为开发复杂动态系统的高效和准确的解决方案提供了有希望的途径.
研究的目的:
- 开发和评估一个创新的智能计算框架,以优化对洛伦兹模型的控制和管理.
- 将人工神经网络与基于无监督学习的随机优化器集成,以提高性能.
- 为了最大限度地降低与解决非线性混乱系统相关的计算成本.
主要方法:
- 莱根德多项式人工神经网络 (LENN) 的实施,用于无监督学习.
- 使用混合方法优化LENN超参数,将火算法 (FA) 和阿基米德优化算法 (AOA) 结合起来,称为LENN-FA-AOA.A.
- 将LENN-FA-AOA框架应用于洛伦茨模型,在三个不同的场景中,不同步骤大小和输入间隔.
- 通过图形模拟和对绝对误差,平均平方误差 (MSE) 和总积标准 (TIC) 的分析进行验证.
主要成果:
- 在不同的场景中,LENN-FA-AOA解决器表现出高精度,绝对误差范围从3.22×10−5到3.06×10−7,4.56×10−5到7.27×10−8,以及5.17×10−5到2.11×10−7.
- 图形模拟证实了拟议的智能解决方案的有效性和稳定性.
- 该方法在洛伦兹模型的各种初始条件下被证明可靠,安全和耐受.
结论:
- 拟议的LENN-FA-AOA框架为管理洛伦茨模型和其他非线性混乱系统提供了有效和准确的解决方案.
- 将LENN与混合FA-AOA优化集成为提高解决复杂动态系统的准确性和效率提供了一种可靠的方法.
- 这种智能设计框架在前神经网络中成功开发了目标/适应性优化功能,验证了其完整性和效率.
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