应用下一代水库计算来从部分观测中预测混乱系统
Irmantas Ratas1, Kestutis Pyragas1
1<a href="https://ror.org/010310r32">Center for Physical Sciences and Technology</a>, LT-10257 Vilnius, Lithuania.
Physical review. E
|July 18, 2024
概括
下一代水库计算有效地利用部分观测预测混乱的系统动态. 用切比舍夫多项式增强特征向量可以提高短期预测和长期气候重建的预测准确度.
科学领域:
- 复杂系统科学 复杂系统科学
- 机器学习 机器学习
- 非线性动力学是一种非线性动力学.
背景情况:
- 储水库计算,一种机器学习技术,显示出预测混乱系统动态的前景.
- 之前的应用主要假定系统状态向量的完全可观测性.
- 使用有限的,标量时间序列数据进行储库计算的有效性仍未得到充分探索.
研究的目的:
- 为了评估下一代储计算的有效性,当只有标量时间序列是可观测的.
- 为了确定最佳的特征向量构造,以改善部分观测的预测准确性.
- 为了证明这些模型对短期预测和长期混乱系统行为重建的能力.
主要方法:
- 应用下一代储存器计算到来自Rössler和Lorenz系统的标量时间序列,以及一个混乱的电子电路.
- 研究特征向量构成的影响,特别是不同度的单项和切比舍夫多项式.
- 利用非线性自回归算法进行时间序列预测和系统状态重建.
主要成果:
- 预测的准确性在很大程度上取决于特征向量内的单项数的程度.
- 用切比舍夫多项式取代单项式大大提高了预测性能.
- 模型成功重建了分叉图和返回图,表明了强大的长期行为预测.
结论:
- 下一代水库计算对于混乱系统的预测是有效的,即使有部分的,标量观测.
- 使用切比舍夫多项式的特征工程对于最大化预测能力至关重要.
- 这种方法为预测和理解复杂系统的长期动态提供了一种可行的方法.
相关概念视频
Classification of Systems-II
138
Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
138
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
48
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...
48
First Order Systems
89
First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
89
State Space Representation
202
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
Consider an RLC circuit, a...
202
Random Error
863
Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
863
Classification of Systems-I
178
Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
178


