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A central challenge in data-driven model discovery is the presence of hidden,or latent, variables that are not directly measured but are dynamicallyimportant. Takens' theorem provides conditions for when it is possible toaugment these partial measurements with time delayed information, resulting inan attractor that is diffeomorphic to that of the original full-state system.However, the coordinate transformation back to the original attractor istypically unknown, and learning the dynamics in the embedding space hasremained an open challenge for decades. Here, we design a custom deepautoencoder network to learn a coordinate transformation from the delayembedded space into a new space where it is possible to represent the dynamicsin a sparse, closed form. We demonstrate this approach on the Lorenz,R\"ossler, and Lotka-Volterra systems, learning dynamics from a singlemeasurement variable. As a challenging example, we learn a Lorenz analogue froma single scalar variable extracted from a video of a chaotic waterwheelexperiment. The resulting modeling framework combines deep learning to uncovereffective coordinates and the sparse identification of nonlinear dynamics(SINDy) for interpretable modeling. Thus, we show that it is possible tosimultaneously learn a closed-form model and the associated coordinate systemfor partially observed dynamics.

Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoders