Unsupervised Learning of Hybrid Latent Dynamics: A Learn-to-Identify Framework
This work addresses the identifiability problem in latent dynamics modeling for applications like physics and biomedical systems, offering a method to incorporate prior knowledge while identifying gaps, though it is incremental in combining existing strategies.
The paper tackles the challenge of unsupervised learning of latent dynamics from high-dimensional time-series by proposing a framework that integrates physics inductive bias and a learn-to-identify strategy, resulting in improved identification of hybrid dynamics as demonstrated through experiments on six systems.
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.