  Physical systems ranging from elastic bodies to kinematic linkages are
defined on high-dimensional configuration spaces, yet their typical low-energy
configurations are concentrated on much lower-dimensional subspaces. This work
addresses the challenge of identifying such subspaces automatically: given as
input an energy function for a high-dimensional system, we produce a
low-dimensional map whose image parameterizes a diverse yet low-energy
submanifold of configurations. The only additional input needed is a single
seed configuration for the system to initialize our procedure; no dataset of
trajectories is required. We represent subspaces as neural networks that map a
low-dimensional latent vector to the full configuration space, and propose a
training scheme to fit network parameters to any system of interest. This
formulation is effective across a very general range of physical systems; our
experiments demonstrate not only nonlinear and very low-dimensional elastic
body and cloth subspaces, but also more general systems like colliding rigid
bodies and linkages. We briefly explore applications built on this formulation,
including manipulation, latent interpolation, and sampling.
