从部分数据中重建,预测和稳定混乱动态
Elise Özalp1, Georgios Margazoglou1, Luca Magri1,2
1Department of Aeronautics, Imperial College London, London SW7 2BX, United Kingdom.
Chaos (Woodbury, N.Y.)
|September 6, 2023
概括
使用长短期内存 (LSTM) 网络的数据驱动方法可以从部分观测中重建混乱的系统动态和稳定性. 这些方法准确地预测隐藏变量并推断稳定性质,优于传统方法.
科学领域:
- 计算物理和应用数学.
- 动态系统理论.动态系统理论.
- 机器学习用于科学发现.
背景情况:
- 传统的基于方程的方法在使用部分数据的混乱系统中难以预测和稳定计算.
- 重建隐藏的动态并从有限的观测中推断稳定性是一个重大挑战.
研究的目的:
- 开发和评估数据驱动的方法,从部分观测中进行混乱系统的全态重建和稳定性分析.
- 用机器学习推断隐藏的混乱动态,并预测系统演变.
- 从不完整的数据计算稳定性质,如利亚普诺夫指数.
主要方法:
- 使用长期短期记忆 (LSTM) 网络,包括低至高分辨率的LSTM (LH-LSTM) 和物理信息的LSTM (PI-LSTM).
- 训练有素的LSTM进行部分状态观测,并结合PI-LSTM的系统动态方程.
- 从LSTM衍生出雅可比式,并分析了诸如Kuramoto-Sivashinsky和Lorenz-96.6之类的混乱系统.
主要成果:
- 拟议的LSTM网络成功地预测了混乱系统中的隐藏变量,具有时间准确性和统计准确性.
- 从部分观测中正确推断出莱普诺夫指数和共变莱普诺夫向量,这是关键稳定性指标.
- 基于物理的LSTM (PI-LSTM) 在重建隐藏的动态方面表现出卓越的性能,特别是在有限的输入尺寸和噪音数据的情况下.
结论:
- 数据驱动的LSTM方法提供了一种可行的替代方案,用于基于部分数据的混乱系统分析的传统方法.
- 开发的PI-LSTM有效地重建隐藏的动态,并推断稳定性质,推进混乱系统建模领域.
- 这项工作为推断隐藏变量和使用不完整的观测数据计算复杂系统中的稳定性提供了新的途径.
相关概念视频
Linear Approximation in Time Domain
100
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
100
Multimachine Stability
188
Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
188
Stability
155
The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
155
Time-Domain Interpretation of PD Control
140
Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
Consider the example of control of motor torque. Initially, a positive...
Consider the example of control of motor torque. Initially, a positive...
140
Pole and System Stability
325
The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's...
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's...
325
BIBO stability of continuous and discrete -time systems
433
System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
433


