Deep reconstruction of strange attractors from time series

Understand

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.