Learning minimal representations of stochastic processes with variational autoencoders

TL;DR

This paper presents an unsupervised variational autoencoder-based method to identify minimal parameters that effectively describe stochastic process dynamics, facilitating better understanding and simulation of complex natural phenomena.

Contribution

The authors introduce a novel extended $eta$-variational autoencoder architecture for unsupervised discovery of minimal parameters in stochastic processes, demonstrated on diffusion models.

Findings

Successfully extracts minimal relevant parameters from simulated diffusion data

Enables generation of realistic stochastic trajectories

Enhances understanding of complex stochastic phenomena

Abstract

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 the autonomous discovery of unknown parameters describing stochastic processes, hence enhancing our comprehension of complex phenomena across various fields.