用深度学习方法实现非线性系统识别，可精准捕捉动态特征。
Data-driven identification of nonlinear dynamical systems with LSTM autoencoders and Normalizing Flows
- 结合LSTM自编码器与归一化流，从时序数据中提取动态特征
- 在杜芬、洛伦兹系统及流体问题上准确关联特征与系统参数
- 适合需要高精度建模的复杂系统设计与控制场景
尽管线性系统已在多个领域发挥作用，但为提升性能与效率，系统正向非线性模式发展。因此，非线性模型对复杂系统的建模、制造与测试至关重要。本文提出基于深度学习的先进非线性系统识别方法，探索了LSTM自编码器和归一化流在提取时序特征并映射至系统参数方面的潜力。该框架为非线性系统识别提供了新思路，能有效处理复杂系统。以杜芬系统、洛伦兹系统以及圆柱绕流和二维顶盖驱动腔流为例进行验证，结果表明该方法能有效捕捉动态特征，并准确建立特征与系统参数间的关联，满足非线性系统识别需求。
原文摘要 · Abstract (English)
While linear systems have been useful in solving problems across different fields, the need for improved performance and efficiency has prompted them to operate in nonlinear modes. As a result, nonlinear models are now essential for the design and control of these systems. However, identifying a nonlinear system is more complicated than identifying a linear one. Therefore, modeling and identifying nonlinear systems are crucial for the design, manufacturing, and testing of complex systems. This study presents using advanced nonlinear methods based on deep learning for system identification. Two deep neural network models, LSTM autoencoder and Normalizing Flows, are explored for their potential to extract temporal features from time series data and relate them to system parameters, respectively. The presented framework offers a nonlinear approach to system identification, enabling it to handle complex systems. As case studies, we consider Duffing and Lorenz systems, as well as fluid flows such as flows over a cylinder and the 2-D lid-driven cavity problem. The results indicate that the presented framework is capable of capturing features and effectively relating them to system parameters, satisfying the identification requirements of nonlinear systems.
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