ODE$^2$VAE: Deep generative second order ODEs with Bayesian neural networks
This addresses the problem of learning complex continuous-time dynamics for sequential data, such as motion capture, with incremental improvements over existing ODE and RNN-based methods.
The paper tackles modeling high-dimensional sequential data by proposing ODE^2VAE, a latent second-order ODE model that decomposes latent space into momentum and position components, achieving state-of-the-art performance in long-term motion prediction and imputation tasks.
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.