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 $ℱ\left(z_{<t};c\right)$ 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 $ℱ\left(z_{<t};c\right)$ 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.