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

Learning latent dynamics is central to assessing current states and forecasting future trajectories for high-dimensional time series. For locally-stationary latent dynamics parameterized by past latent states and an environment variable c, with latent dynamics state zt, prior identifiability results largely focus on zt when conditioned on pre-defined label u of the dynamics environment. This leaves two limitations: reliance on pre-defined labels that hinder generalization to unseen environments, and limited understanding of the identifiability of F and c which---while offering important structural properties for the identifiability of zt---are learned jointly with zt. We address these challenges with Meta-iLaD, a novel latent dynamics framework to attain identifiability by meta-learning across dynamics environments. Meta-iLaD replaces the conditioning of c on pre-defined labels with a novel conditional prior, modeled as a feedforward meta-learner that rapidly extracts c from few-shot examples. We further establish simultaneous identifiability for z_t, c and F, for a general formulation of the dynamics function F over past latent states and c, without restricting the dimension of c or how it modulates F. 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.

Many real-world systems — such as climate, finance, and biological processes — evolve over time in ways that are hard to observe directly. Learning the hidden dynamics behind these systems is key to understanding their current state and predicting their future behavior. Existing approaches, however, require pre-defined labels to identify different dynamic environments, limiting their ability to generalize to new, unseen scenarios. We propose Meta-iLaD, a framework that learns to rapidly adapt to new dynamic environments from just a few examples, without relying on any pre-defined labels. We also provide theoretical guarantees that our method correctly identifies the underlying dynamics structure. Experiments show that Meta-iLaD generalizes well to out-of-distribution environments and produces more accurate forecasts compared to existing methods.