Reviews: Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition

This paper presents a method that takes advantage of MLPs to learning non-linear functions that support Koopman analysis of time-series data. The framework is based on Koopman operator theory, an observation that complex, nonlinear dynamics may be embedded with nonlinear functions g where a spectral properties of a linear operator K can be informative about both the dynamics of the system and predict future data. The paper proposes a neural network architecture and a set of loss functions suitable for learning this embedding in a Koopman invariant subspace, directly from data. The method is demonstrate both on numerical examples and on a few applications (Lorenz, Rossler, and unstable phenomena data). The paper is exceptionally clearly written, and the use of a neural network for finding Koopman invariant subspaces, a challenging and widely applicable task, is well motivated.