Accurate and efficient fluid flow models are essential for applications relating to many physical phenomena including geophysical, aerodynamic, and biological systems. While these flows may exhibit rich and multiscale dynamics, in many cases underlying low-rank structures exist which describe the bulk of the motion. These structures tend to be spatially large and temporally slow, and may contain most of the energy in a given flow. The extraction and parsimonious representation of these low-rank dynamics from high-dimensional data is a key challenge. Inspired by the success of physics-informed machine learning methods, we propose a spectrally-informed approach to extract low-rank models of fluid flows by leveraging known spectral properties in the learning process. We incorporate this knowledge by imposing regularizations on the learned dynamics, which bias the training process towards learning low-frequency structures with corresponding higher power. We demonstrate the effectiveness of this method to improve prediction and produce learned models which better match the underlying spectral properties of prototypical fluid flows.

本文解决了从高维数据中提取流体流动的低秩动态这一关键挑战，采用了一种基于光谱信息的学习方法。通过在学习过程中引入已知的光谱性质，从而更好地捕捉低频结构，显著提高了预测精度并使所学模型更符合流体流动的光谱特性。

光谱信息驱动的流体流动学习