Classification, inference and segmentation of anomalous diffusion with recurrent neural networks

Abstract: Countless systems in biology, physics, and finance undergo diffusive dynamics. Many of these systems, including biomolecules inside cells, active matter systems and foraging animals, exhibit anomalous dynamics where the growth of the mean squared displacement with time follows a power law with an exponent that deviates from $1$. When studying time series recording the evolution of these systems, it is crucial to precisely measure the anomalous exponent and confidently identify the mechanisms responsible for anomalous diffusion. These tasks can be overwhelmingly difficult when only few short trajectories are available, a situation that is common in the study of non-equilibrium and living systems. Here, we present a data-driven method to analyze single anomalous diffusion trajectories employing recurrent neural networks, which we name RANDI. We show that our method can successfully infer the anomalous exponent, identify the type of anomalous diffusion process, and segment the trajectories of systems switching between different behaviors. We benchmark our performance against the state-of-the art techniques for the study of single short trajectories that participated in the Anomalous Diffusion (AnDi) Challenge. Our method proved to be the most versatile method, being the only one to consistently rank in the top 3 for all tasks proposed in the AnDi Challenge.