  Neural Stochastic Differential Equations (NSDE) have been trained as both
Variational Autoencoders, and as GANs. However, the resulting Stochastic
Differential Equations can be hard to interpret or analyse due to the generic
nature of the drift and diffusion fields. By restricting our NSDE to be of the
form of Langevin dynamics, and training it as a VAE, we obtain NSDEs that lend
themselves to more elaborate analysis and to a wider range of visualisation
techniques than a generic NSDE. More specifically, we obtain an energy
landscape, the minima of which are in one-to-one correspondence with latent
states underlying the used data. This not only allows us to detect states
underlying the data dynamics in an unsupervised manner, but also to infer the
distribution of time spent in each state according to the learned SDE. More in
general, restricting an NSDE to Langevin dynamics enables the use of a large
set of tools from computational molecular dynamics for the analysis of the
obtained results.
