Learning physical properties of anomalous random walks using graph neural networks

TL;DR

This paper introduces a fast, graph neural network-based method for inferring physical properties of anomalous random walks from single particle trajectories, overcoming challenges of noise and short data length.

Contribution

The paper presents a novel GNN approach that reliably learns random walk models and anomalous exponents from trajectories of any length, outperforming existing methods.

Findings

Accurately infers random walk models and exponents

Effective on biological anomalous random walks from the AnDi challenge

Maintains high accuracy with limited training parameters

Abstract

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.