Hamiltonian systems possess several crucial properties, such as a symplectic flow and energy preservation. The preservation of these properties in numerical models can lead to more accurate and stable simulations. In this talk, we present data-driven modeling for nonlinear Hamiltonian systems. This approach enables the construction of simpler models, thereby facilitating prediction, control, and optimization for complex nonlinear Hamiltonian systems. In line with our objective, Koopman operator theory provides a framework for the global linearization of nonlinear systems, which allows for the use of linear tools in design studies. In this work, our focus is on identifying global linearized embeddings for canonical nonlinear Hamiltonian systems through a symplectic transformation. While this task can be challenging, we utilize the strength of deep learning to uncover the desired embeddings. To address the constraints of Koopman operators in systems with continuous spectra, we implement the lifting principle and acquire global cubic embeddings. Furthermore, we emphasize the importance of ensuring stability in the dynamics of the discovered embeddings. We showcase the potential of deep learning in obtaining compact symplectic coordinate transformations and their corresponding simplistic dynamical models. This promotes data-driven learning of nonlinear canonical Hamiltonian systems, even those possessing continuous spectra.