🤖 AI Summary
This work addresses the challenge of identifying latent dynamical systems and recovering their governing equations from noisy, high-dimensional observations. The authors propose DYSCO, a novel method that uniquely integrates multi-view temporal contrastive learning with structured function basis parameterization. DYSCO establishes strong identifiability of the latent dynamics—up to affine equivalence—even under nonlinear observations, and enables symbolic equation discovery. By performing symbolic regression within an affine-normalized representation, DYSCO accurately reconstructs both latent trajectories and vector fields. The method demonstrates robust performance across diverse dynamical regimes, including chaotic, oscillatory, and metastable systems, and handles both Gaussian and Poisson noise, with the latter being particularly relevant for neural recording data.
📝 Abstract
Identifying latent dynamical systems from noisy, high-dimensional measurements is a central problem at the intersection of representation learning, system identification, and scientific discovery. We present DYSCO, a multi-view temporal contrastive learning algorithm that jointly recovers latent trajectories and the governing dynamics from such observations, by leveraging multiple independent noisy views of the same underlying process to disentangle signal from noise. By parameterizing the dynamics in a structured functional basis, our framework further enables symbolic recovery of the governing equations within an affine gauge. We offer theoretical guarantees for strong identification up to an affine indeterminacy, extending prior identifiability results to the realistic setting of noisy nonlinear observations. Empirically, we demonstrate accurate recovery of both latent trajectories and flow fields across a diverse set of dynamical regimes (e.g., chaotic, oscillatory, and metastable) under both Gaussian and Poisson observation noise, the latter being particularly relevant for neural recordings.