  Experimental measurements of physical systems often have a limited number of
independent channels, causing essential dynamical variables to remain
unobserved. However, many popular methods for unsupervised inference of latent
dynamics from experimental data implicitly assume that the measurements have
higher intrinsic dimensionality than the underlying system---making coordinate
identification a dimensionality reduction problem. Here, we study the opposite
limit, in which hidden governing coordinates must be inferred from only a
low-dimensional time series of measurements. Inspired by classical analysis
techniques for partial observations of chaotic attractors, we introduce a
general embedding technique for univariate and multivariate time series,
consisting of an autoencoder trained with a novel latent-space loss function.
We show that our technique reconstructs the strange attractors of synthetic and
real-world systems better than existing techniques, and that it creates
consistent, predictive representations of even stochastic systems. We conclude
by using our technique to discover dynamical attractors in diverse systems such
as patient electrocardiograms, household electricity usage, neural spiking, and
eruptions of the Old Faithful geyser---demonstrating diverse applications of
our technique for exploratory data analysis.
