Identifying latent state transition in non-linear dynamical systems

TL;DR

This paper introduces a novel state-space modeling framework using variational auto-encoders to identify nonlinear latent state transitions in dynamical systems, enhancing prediction accuracy and adaptability.

Contribution

It extends nonlinear ICA techniques to dynamical systems, enabling the recovery of both latent states and their nonlinear transition functions.

Findings

High accuracy in recovering latent state dynamics

Improved future prediction accuracy

Fast adaptation to new environments

Abstract

This work aims to improve generalization and interpretability of dynamical systems by recovering the underlying lower-dimensional latent states and their time evolutions. Previous work on disentangled representation learning within the realm of dynamical systems focused on the latent states, possibly with linear transition approximations. As such, they cannot identify nonlinear transition dynamics, and hence fail to reliably predict complex future behavior. Inspired by the advances in nonlinear ICA, we propose a state-space modeling framework in which we can identify not just the latent states but also the unknown transition function that maps the past states to the present. We introduce a practical algorithm based on variational auto-encoders and empirically demonstrate in realistic synthetic settings that we can (i) recover latent state dynamics with high accuracy, (ii) correspondingly achieve high future prediction accuracy, and (iii) adapt fast to new environments.