ODE$^2$VAE: Deep generative second order ODEs with Bayesian neural networks

TL;DR

ODE$^2$VAE introduces a second order ODE-based deep generative model with Bayesian neural networks for high-dimensional sequential data, enabling better long-term predictions and uncertainty quantification.

Contribution

It proposes a novel second order ODE latent model with Bayesian neural networks, explicitly modeling momentum and position for improved sequential data analysis.

Findings

State-of-the-art long-term motion prediction accuracy

Effective imputation of missing data in sequences

Robust uncertainty estimation in latent dynamics

Abstract

We present Ordinary Differential Equation Variational Auto-Encoder (ODE$^2$VAE), a latent second order ODE model for high-dimensional sequential data. Leveraging the advances in deep generative models, ODE$^2$VAE can simultaneously learn the embedding of high dimensional trajectories and infer arbitrarily complex continuous-time latent dynamics. Our model explicitly decomposes the latent space into momentum and position components and solves a second order ODE system, which is in contrast to recurrent neural network (RNN) based time series models and recently proposed black-box ODE techniques. In order to account for uncertainty, we propose probabilistic latent ODE dynamics parameterized by deep Bayesian neural networks. We demonstrate our approach on motion capture, image rotation and bouncing balls datasets. We achieve state-of-the-art performance in long term motion prediction and imputation tasks.