Meta-iLaD: Identifiable Latent Dynamics via Meta-Learning of Dynamics Environments.

Learning latent dynamics is central to assessing the current states and forecasting the future trajectories of high-dimensional time series. For locally-stationary latent dynamics ℱ z < t ; c with latent dynamics state z t and environment variable c , prior identifiability results have largely focused on z t when conditioned on predefined label u of dynamics environments. This leaves two limitations: reliance on predefined labels that hinder generalization to unseen environments, and a limited understanding of the identifiability of ℱ and c which-although offering important structural properties for the identifiability of z t -are learned jointly with z t . We address these limitations with Meta-iLaD, a novel identifiable latent dynamics framework attained by meta-learning across dynamics environments. Meta-iLaD introduces a novel conditional prior of c , modeled as a feedforward meta-learner to rapidly extract c from few-shot examples. Meta-iLaD further establishes identifiability for z t , c , and ℱ simultaneously, for a general formulation of ℱ z < t ; c without restricting the dimension of c or how it modulates ℱ . On synthetic and real data, we provide strong empirical evidence that 1) conditioning on few-shot examples enables generalization to out-of-distribution environments, and 2) identifiability for c and ℱ is critical for accurate forecasting beyond reconstructing observed trajectories.