AI Insight
This paper introduces DYSCO, a machine learning algorithm that can identify underlying dynamical systems from noisy, high-dimensional data by using multiple independent observations of the same process. The method simultaneously recovers both the hidden trajectories and the mathematical equations governing the system's behavior, with theoretical guarantees for identification accuracy. The approach was validated on various types of dynamics including chaotic and oscillatory systems, showing successful recovery under different noise conditions including those relevant to neural data.
Why it matters
This work has significant implications for scientific fields where researchers need to extract fundamental laws from noisy measurements, such as neuroscience, climate modeling, and complex systems biology. By enabling automatic discovery of governing equations from real-world data, it could accelerate scientific discovery and improve our ability to model and predict complex natural phenomena.
Understand the Science
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.
Source: Extracting Governing Equations from Latent Dynamics via Multi-View Contrastive Learning