Unsupervised Learning of Hybrid Latent Dynamics: A Learn-to-Identify
  Framework
Yubo Ye Sumeet Vadhavkar Xiajun Jiang Ryan Missel Huafeng Liu Linwei Wang
Modern applications increasingly require unsupervised learning of latent
dynamics from high-dimensional time-series. This presents a significant
challenge of identifiability: many abstract latent representations may
reconstruct observations, yet do they guarantee an adequate identification of
the governing dynamics? This paper investigates this challenge from two angles:
the use of physics inductive bias specific to the data being modeled, and a
learn-to-identify strategy that separates forecasting objectives from the data
used for the identification. We combine these two strategies in a novel
framework for unsupervised meta-learning of hybrid latent dynamics (Meta-HyLaD)
with: 1) a latent dynamic function that hybridize known mathematical
expressions of prior physics with neural functions describing its unknown
errors, and 2) a meta-learning formulation to learn to separately identify both
components of the hybrid dynamics. Through extensive experiments on five
physics and one biomedical systems, we provide strong evidence for the benefits
of Meta-HyLaD to integrate rich prior knowledge while identifying their gap to
observed data.