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

Leveraging Neural Koopman Operators to Learn Continuous Representations of Dynamical Systems from Scarce Data