蜂群和内部点算法的混合,以解决拉比诺维奇-法布里坎特系统
Zulqurnain Sabir1, Salem Ben Said2, Qasem Al-Mdallal1
1Department of Mathematical Sciences, College of Science, United Arab Emirates University, P. O. Box 15551, Al Ain, UAE.
Scientific reports
|July 6, 2023
概括
一个新的人工神经网络 (ANN) 与粒子群优化 (PSO) 和内部点 (IP) 算法有效地解决了拉比诺维奇-法布里坎特系统. 这种ANNs-PSOIP方法在复杂的非线性动态中实现了高精度.
科学领域:
- 计算物理 计算物理
- 非线性动力学是一种非线性动力学.
- 人工智能的人工智能
背景情况:
- 拉比诺维奇-法布里坎特系统是一个复杂的非线性动态系统,由三个微分方程描述.
- 解决这样的系统往往需要强大而准确的计算方法.
- 群体计算为解决复杂的数学模型提供了一种强大的方法.
研究的目的:
- 为拉比诺维奇-法布里坎特系统引入一种可靠的群体计算程序.
- 开发和验证用于非线性动态的混合计算模型.
- 评估拟议方法的准确性和一致性.
主要方法:
- 使用集成人工神经网络 (ANN) 的计算随机结构.
- 全球搜索使用粒子群优化 (PSO) 结合本地内部点 (IP) 算法进行.
- 该ANNs-PSOIP混合模型优化了从系统的微分方程中得出的客观函数.
主要成果:
- 该ANNs-PSOIP方案在解决拉比诺维奇-法布里坎特系统方面表现出高度准确性.
- 获得的解决方案与源解决方案密切匹配,绝对误差在10-05-10-07之间是可以忽略不计的.
- 统计程序证实了ANNs-PSOIP方法的一致性和可靠性.
结论:
- 开发的ANNs-PSOIP方法为非线性动态提供了可靠和高效的计算解决方案.
- 混合模型有效地结合了ANN,PSO和IP算法的优势.
- 这种方法为分析像拉比诺维奇-法布里坎特系统这样的复杂动态系统提供了有价值的工具.
相关概念视频
Hybridization of Atomic Orbitals II
32.6K
sp3d and sp3d 2 Hybridization
32.6K
Hybridization of Atomic Orbitals I
47.4K
The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...
47.4K
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
81
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
81
Routh-Hurwitz Criterion II
299
In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
299
Hybrid Zones
17.1K
Hybrid zones are narrow regions where two closely related species interact, mate, and produce hybrids. Relative to either parent species, hybrids may possess distinct phenotypic or genetic differences that impact their survival and reproductive success. The genetic variances introduced by hybridization influence species diversity and speciation processes within the hybrid zone.
17.1K
Statically Indeterminate Problem Solving
455
Statically indeterminate problems are those where statics alone can not determine the internal forces or reactions. Consider a structure comprising two cylindrical rods made of steel and brass. These rods are joined at point B and restrained by rigid supports at points A and C. Now, the reactions at points A and C and the deflection at point B are to be determined. This rod structure is classified as statically indeterminate as the structure has more supports than are necessary for maintaining...
455


