Abstract. Owing to their data-efficiency, sparse Gaussian process methods have proven to be a promising approach for tasks such as modeling of dynamical systems in robotics. In spite of this, their use in large-scale reinforcement learning remains limited, when compared to deep Q-learning. We present recent work that uses physically-meaningful deep networks to construct data-efficient embeddings of dynamical systems. We illustrate theoretical and computational issues that arise when attempting to apply similar constructions to obtain physically-meaningful Gaussian processes with dimensionally-efficient behavior. We conclude with a discussion on strategies for addressing these issues.