Leveraging Neural Koopman Operators to Learn Continuous Representations of Dynamical Systems from Scarce Data
This addresses the challenge of data loss in discretized methods for researchers in dynamical systems modeling, though it appears incremental.
The paper tackled the problem of learning dynamical systems from scarce data by proposing a new deep Koopman framework that represents dynamics continuously, resulting in better performance on limited training data across several datasets.
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.