Latent Space Energy-based Neural ODEs

TL;DR

This paper presents a novel deep dynamical model combining neural ODEs and energy-based priors to effectively model continuous-time sequences, disentangle static and dynamic factors, and improve long-term prediction accuracy.

Contribution

It introduces a new framework integrating neural ODEs with energy-based priors and static-dynamic disentanglement for continuous-time sequence modeling.

Findings

Outperforms existing models on oscillating systems, videos, and MuJoCo data.

Enables generalization to new dynamic parameters.

Provides accurate long-horizon predictions.

Abstract

This paper introduces novel deep dynamical models designed to represent continuous-time sequences. Our approach employs a neural emission model to generate each data point in the time series through a non-linear transformation of a latent state vector. The evolution of these latent states is implicitly defined by a neural ordinary differential equation (ODE), with the initial state drawn from an informative prior distribution parameterized by an Energy-based model (EBM). This framework is extended to disentangle dynamic states from underlying static factors of variation, represented as time-invariant variables in the latent space. We train the model using maximum likelihood estimation with Markov chain Monte Carlo (MCMC) in an end-to-end manner. Experimental results on oscillating systems, videos and real-world state sequences (MuJoCo) demonstrate that our model with the learnable energy-based prior outperforms existing counterparts, and can generalize to new dynamic parameterization, enabling long-horizon predictions.