  Many dynamical systems exhibit similar structure, as often captured by
hand-designed simplified models that can be used for analysis and control. We
develop a method for learning to correspond pairs of dynamical systems via a
learned latent dynamical system. Given trajectory data from two dynamical
systems, we learn a shared latent state space and a shared latent dynamics
model, along with an encoder-decoder pair for each of the original systems.
With the learned correspondences in place, we can use a simulation of one
system to produce an imagined motion of its counterpart. We can also simulate
in the learned latent dynamics and synthesize the motions of both corresponding
systems, as a form of bisimulation. We demonstrate the approach using pairs of
controlled bipedal walkers, as well as by pairing a walker with a controlled
pendulum.
