Learning minimal representations of stochastic processes with variational autoencoders

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.

10 pages, 5 figures, 1 table. Code available at https://github.com/GabrielFernandezFernandez/SPIVAE . Updated to journal version

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Cited by in corpus (4)

• Machine Learning Analysis of Anomalous Diffusion
• Machine learning stochastic differential equations for the evolution of order parameters of classical many-body systems in and out of equilibrium
• Recurrent neural network analysis of single trajectories switching between anomalous diffusion states
• Interpretable representation learning of quantum data enabled by probabilistic variational autoencoders