  Stochastic processes have found numerous applications in science, as they are
broadly used to model a variety of natural phenomena. Due to their intrinsic
randomness and uncertainty, they are however difficult to characterize. Here,
we introduce an unsupervised machine learning approach to determine the minimal
set of parameters required to effectively describe the dynamics of a stochastic
process. Our method builds upon an extended $\beta$-variational autoencoder
architecture. By means of simulated datasets corresponding to paradigmatic
diffusion models, we showcase its effectiveness in extracting the minimal
relevant parameters that accurately describe these dynamics. Furthermore, the
method enables the generation of new trajectories that faithfully replicate the
expected stochastic behavior. Overall, our approach enables for the autonomous
discovery of unknown parameters describing stochastic processes, hence
enhancing our comprehension of complex phenomena across various fields.

Soft Condensed Matter;Machine Learning;Biological Physics;Data Analysis, Statistics and Probability;Quantitative Methods