论文标题
神经动态模式分解，用于非线性动力学的端到端建模
Neural Dynamic Mode Decomposition for End-to-End Modeling of Nonlinear Dynamics
论文作者
论文摘要
Koopman光谱分析引起了人们对了解非线性动力学系统的关注，我们可以通过使用非线性函数提升观测值来通过线性制度分析非线性动力学。为了进行分析，我们需要找到适当的提升功能。尽管已经提出了几种基于神经网络的升力函数的方法，但现有方法训练神经网络而无需光谱分析。在本文中，我们提出了神经动态模式分解，其中对神经网络进行了训练，从而使预测误差在基于升高空间中的光谱分解建模时最小化。通过我们提出的方法，通过神经网络和光谱分解将预测误差反向传播，从而实现了Koopman光谱分析的端到端学习。当提供有关动态频率或增长率的信息时，提出的方法可以将其作为训练的正规化器来利用它。当观测受到外在控制时间序列的影响时，我们还提出了我们的方法的扩展。我们的实验证明了我们提出的方法在特征值估计和预测性能方面的有效性。
Koopman spectral analysis has attracted attention for understanding nonlinear dynamical systems by which we can analyze nonlinear dynamics with a linear regime by lifting observations using a nonlinear function. For analysis, we need to find an appropriate lift function. Although several methods have been proposed for estimating a lift function based on neural networks, the existing methods train neural networks without spectral analysis. In this paper, we propose neural dynamic mode decomposition, in which neural networks are trained such that the forecast error is minimized when the dynamics is modeled based on spectral decomposition in the lifted space. With our proposed method, the forecast error is backpropagated through the neural networks and the spectral decomposition, enabling end-to-end learning of Koopman spectral analysis. When information is available on the frequencies or the growth rates of the dynamics, the proposed method can exploit it as regularizers for training. We also propose an extension of our approach when observations are influenced by exogenous control time-series. Our experiments demonstrate the effectiveness of our proposed method in terms of eigenvalue estimation and forecast performance.
