Koopman-Based Learning of Infinitesimal Generators without Operator Logarithm

To retrieve transient transition information of unknown systems from discrete-time observations, the Koopman operator structure has gained significant attention in recent years, particularly for its ability to avoid time derivatives through the Koopman operator logarithm. However, the effectiveness of these logarithm-based methods has only been demonstrated within a restrictive function space. In this paper, we propose a logarithm-free technique for learning the infinitesimal generator without disrupting the Koopman operator learning framework.