# Learning to Correspond Dynamical Systems

arXiv: https://arxiv.org/abs/1912.03015 · HTML: https://mlsanity.com/paper/1912.03015/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Dec 2019.

## Built on by (most cited first, 4 of 4)

- [Polybot: Training One Policy Across Robots While Embracing Variability](https://mlsanity.com/paper/2307.03719/) (2023)
- [FLD: Fourier Latent Dynamics for Structured Motion Representation and Learning](https://mlsanity.com/paper/2402.13820/) (2024)
- [Invariance Co-training for Robot Visual Generalization](https://mlsanity.com/paper/2512.05230/) (2025)
- [Temporal Basis Function Models for Closed-Loop Neural Stimulation](https://mlsanity.com/paper/2507.15274/) (2025)

## Abstract (arXiv)

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.