PyKoopman is a Python package for the data-driven approximation of the
Koopman operator associated with a dynamical system. The Koopman operator is a
principled linear embedding of nonlinear dynamics and facilitates the
prediction, estimation, and control of strongly nonlinear dynamics using linear
systems theory. In particular, PyKoopman provides tools for data-driven system
identification for unforced and actuated systems that build on the
equation-free dynamic mode decomposition (DMD) and its variants. In this work,
we provide a brief description of the mathematical underpinnings of the Koopman
operator, an overview and demonstration of the features implemented in
PyKoopman (with code examples), practical advice for users, and a list of
potential extensions to PyKoopman. Software is available at
this http URL

PyKoopman 是用于数据驱动的动力系统 Koopman 算子近似的 Python 包，提供了基于动态模式分解 (DMD) 和其变体的无方程动态模态分解的数据驱动系统辨识工具。

PyKoopman：一款用于数据驱动的 Koopman 算子逼近的 Python 包

PyKoopman: A Python Package for Data-Driven Approximation of the Koopman  Operator

We develop a general framework for data-driven approximation of input-output
maps between infinite-dimensional spaces. The proposed approach is motivated by
the recent successes of neural networks and deep learning, in combination with
ideas from model reduction. This combination results in a neural network
approximation which, in principle, is defined on infinite-dimensional spaces
and, in practice, is robust to the dimension of finite-dimensional
approximations of these spaces required for computation. For a class of
input-output maps, and suitably chosen probability measures on the inputs, we
prove convergence of the proposed approximation methodology. We also include
numerical experiments which demonstrate the effectiveness of the method,
showing convergence and robustness of the approximation scheme with respect to
the size of the discretization, and compare it with existing algorithms from
the literature; our examples include the mapping from coefficient to solution
in a divergence form elliptic partial differential equation (PDE) problem, and
the solution operator for viscous Burgers' equation.

发展了一种数据驱动输入输出图像无限维空间的近似方法，使用了神经网络和深度学习并结合模型缩减的思想，该方法在概念上定义于无限维空间上，并在实践中对计算所需的有限维空间的维度稳健，通过对输入输出映射的一类概率测度的选择，证明了所提出近似方法的收敛性。数值实验表明了该方法的有效性，并将其与现有的算法相比较。