  Single particle tracking allows probing how biomolecules interact physically
with their natural environments. A fundamental challenge when analysing
recorded single particle trajectories is the inverse problem of inferring the
physical model or class of models of the underlying random walks. Reliable
inference is made difficult by the inherent stochastic nature of single
particle motion, by experimental noise, and by the short duration of most
experimental trajectories. Model identification is further complicated by the
fact that main physical properties of random walk models are only defined
asymptotically, and are thus degenerate for short trajectories. Here, we
introduce a new, fast approach to inferring random walk properties based on
graph neural networks (GNNs). Our approach consists in associating a vector of
features with each observed position, and a sparse graph structure with each
observed trajectory. By performing simulation-based supervised learning on this
construct [1], we show that we can reliably learn models of random walks and
their anomalous exponents. The method can naturally be applied to trajectories
of any length. We show its efficiency in analysing various anomalous random
walks of biological relevance that were proposed in the AnDi challenge [2]. We
explore how information is encoded in the GNN, and we show that it learns
relevant physical features of the random walks. We furthermore evaluate its
ability to generalize to types of trajectories not seen during training, and we
show that the GNN retains high accuracy even with few parameters. We finally
discuss the possibility to leverage these networks to analyse experimental
data.
