Over the last few years, several works have proposed deep learning architectures to learn dynamical systems from observation data with no or little knowledge of the underlying physics. A line of work relies on learning representations where the dynamics of the underlying phenomenon can be described by a linear operator, based on the Koopman operator theory. However, despite being able to provide reliable long-term predictions for some dynamical systems in ideal situations, the methods proposed so far have limitations, such as requiring to discretize intrinsically continuous dynamical systems, leading to data loss, especially when handling incomplete or sparsely sampled data. Here, we propose a new deep Koopman framework that represents dynamics in an intrinsically continuous way, leading to better performance on limited training data, as exemplified on several datasets arising from dynamical systems.

翻译：近年来，多项研究提出了基于深度学习的架构，能够在几乎不了解底层物理机制的情况下，从观测数据中学习动力系统。其中一条研究路线借助Koopman算子理论，学习可用线性算子描述底层现象动态的表示。然而，尽管这些方法在理想情况下能对某些动力系统提供可靠的长时预测，但它们存在局限性，例如需要离散化本质连续的动力系统，这在处理不完整或稀疏采样数据时会导致信息损失。本文提出了一种新的深度Koopman框架，以本质连续的方式表示动态，从而在有限的训练数据上取得更优性能，这在多个动力系统数据集上得到了验证。