论文标题
学到的提起的线性化应用于Koopman直接编码启用的不稳定动态系统
Learned Lifted Linearization Applied to Unstable Dynamic Systems Enabled by Koopman Direct Encoding
论文作者
论文摘要
本文提出了一种Koopman提升线性化方法，该方法适用于具有稳定区域和不稳定区域的非线性动力学系统。众所周知，当应用于不稳定系统时，DMD和其他标准数据驱动的方法在构建Koopman模型方面面临着根本的困难。在这里，我们通过将有关非线性状态方程的知识与找到有效的可观察结果集的学习方法结合在一起来解决问题。在提升的空间中，稳定和不稳定的区域分为独立的子空间。基于此属性，我们建议通过神经净训练找到有效的可观察物，其中训练数据被分为稳定且不稳定的轨迹。所得学习的可观察物用于使用称为直接编码的方法构建线性状态过渡矩阵，该方法通过使用可观测值的内部产品计算将非线性状态方程转换为状态过渡矩阵。提出的方法显示了对现有DMD和数据驱动方法的显着改善。
This paper presents a Koopman lifting linearization method that is applicable to nonlinear dynamical systems having both stable and unstable regions. It is known that DMD and other standard data-driven methods face a fundamental difficulty in constructing a Koopman model when applied to unstable systems. Here we solve the problem by incorporating knowledge about a nonlinear state equation with a learning method for finding an effective set of observables. In a lifted space, stable and unstable regions are separated into independent subspaces. Based on this property, we propose to find effective observables through neural net training where training data are separated into stable and unstable trajectories. The resultant learned observables are used for constructing a linear state transition matrix using method known as Direct Encoding, which transforms the nonlinear state equation to a state transition matrix through inner product computations with the observables. The proposed method shows a dramatic improvement over existing DMD and data-driven methods.
