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

27 May 2019  ·  Çağatay Yıldız, Markus Heinonen, Harri Lähdesmäki ·

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.

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Results from the Paper

Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Video Prediction CMU Mocap-1 ODE2VAE-KL Test Error 15.99 # 1
Video Prediction CMU Mocap-1 ODE2VAE Test Error 93.07 # 2
Video Prediction CMU Mocap-2 ODE2VAE Test Error 10.06 # 4
Video Prediction CMU Mocap-2 ODE2VAE-KL Test Error 8.09 # 3


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