# Analysis of ODE2VAE with Examples

arXiv: https://arxiv.org/abs/2108.04899 · HTML: https://mlsanity.com/paper/2108.04899/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 38 references that are in the map.
- First posted on arXiv 10 Aug 2021.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Inductive Biases for Deep Learning of Higher-Level Cognition](https://mlsanity.com/paper/2011.15091/) (2020)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [GP-VAE: Deep Probabilistic Time Series Imputation](https://mlsanity.com/paper/1907.04155/) (2019)
- [Isolating Sources of Disentanglement in Variational Autoencoders](https://mlsanity.com/paper/1802.04942/) (2018)
- [Bayesian Convolutional Neural Networks with Bernoulli Approximate Variational Inference](https://mlsanity.com/paper/1506.02158/) (2015)
- [Hamiltonian Generative Networks](https://mlsanity.com/paper/1909.13789/) (2019)
- [Learning to Decompose and Disentangle Representations for Video Prediction](https://mlsanity.com/paper/1806.04166/) (2018)
- [Disentangled Sequential Autoencoder](https://mlsanity.com/paper/1803.02991/) (2018)
- [A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learning](https://mlsanity.com/paper/1710.05741/) (2017)
- [An Introduction to Deep Generative Modeling](https://mlsanity.com/paper/2103.05180/) (2021)
- [An Uncertain Future: Forecasting from Static Images using Variational Autoencoders](https://mlsanity.com/paper/1606.07873/) (2016)
- [Bayesian Neural Ordinary Differential Equations](https://mlsanity.com/paper/2012.07244/) (2020)
- [ODE2VAE: Deep generative second order ODEs with Bayesian neural networks](https://mlsanity.com/paper/1905.10994/) (2019)
- [A Variational Auto-Encoder Model for Stochastic Point Processes](https://mlsanity.com/paper/1904.03273/) (2019)
- [Neural Ordinary Differential Equations for Intervention Modeling](https://mlsanity.com/paper/2010.08304/) (2020)

## Abstract (arXiv)

Deep generative models aim to learn underlying distributions that generate the observed data. Given the fact that the generative distribution may be complex and intractable, deep latent variable models use probabilistic frameworks to learn more expressive joint probability distributions over the data and their low-dimensional hidden variables. Learning complex probability distributions over sequential data without any supervision is a difficult task for deep generative models. Ordinary Differential Equation Variational Auto-Encoder (ODE2VAE) is a deep latent variable model that aims to learn complex distributions over high-dimensional sequential data and their low-dimensional representations. ODE2VAE infers continuous latent dynamics of the high-dimensional input in a low-dimensional hierarchical latent space. The hierarchical organization of the continuous latent space embeds a physics-guided inductive bias in the model. In this paper, we analyze the latent representations inferred by the ODE2VAE model over three different physical motion datasets: bouncing balls, projectile motion, and simple pendulum. Through our experiments, we explore the effects of the physics-guided inductive bias of the ODE2VAE model over the learned dynamical latent representations. We show that the model is able to learn meaningful latent representations to an extent without any supervision.