Nam Hee Kim, Zhaoming Xie, Michiel van de Panne
University of British Columbia
Oral presentation at Learning for Dynamics and Control (L4DC) 2020.
Please use the following BibTex to cite our work:
@InProceedings{pmlr-v120-kim20a, title = {Learning to Correspond Dynamical Systems}, author = {Kim, Nam Hee and Xie, Zhaoming and van de Panne, Michiel}, pages = {105--117}, year = {2020}, editor = {Alexandre M. Bayen and Ali Jadbabaie and George Pappas and Pablo A. Parrilo and Benjamin Recht and Claire Tomlin and Melanie Zeilinger}, volume = {120}, series = {Proceedings of Machine Learning Research}, address = {The Cloud}, month = {10--11 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v120/kim20a/kim20a.pdf}, url = {http://proceedings.mlr.press/v120/kim20a.html}}
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.
Using state trajectories to learn dynamics
Abstract view of variables and learned mappings
Summary of loss functions