  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.
