Most real-world dynamical systems exhibit nonlinear behavior, while many well-established analysis and control methods are designed for linear systems. Koopman operator theory provides a framework for representing nonlinear dynamical systems as approximately linear systems in a higher-dimensional space through nonlinear observable functions. However, identifying suitable observable functions for general nonlinear systems remains an open research problem. In this project, we investigate reinforcement learning and representation learning methods to discover Koopman observable functions. The goal is to learn representations that capture the nonlinear dynamics while allowing the system evolution to be described by a higher-dimensional linear model. Once appropriate observable functions are obtained, established linear-system methods can be used for analysis and controller design. The resulting controllers can then be evaluated on the original nonlinear system. Learning these observable functions requires generating large amounts of simulation data and repeatedly training and evaluating learning algorithms. These experiments can be computationally demanding, particularly when testing different model architectures, parameters, and training strategies. High-performance computing resources would allow us to run simulations in parallel and accelerate neural-network and reinforcement-learning training. As a next step, we plan to evaluate the proposed methods on more complex reinforcement learning environments, such as HalfCheetah. This will allow us to study whether the learned Koopman representations can be applied effectively to higher-dimensional nonlinear control problems.