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.

单粒子跟踪允许探索生物分子如何与其自然环境进行物理相互作用。分析记录的单粒子轨迹时的一个基本挑战是推断潜在随机游走的物理模型或模型类别的逆问题。由于单粒子运动固有的随机性、实验噪声以及大多数实验轨迹的持续时间短，难以进行可靠的推理。由于随机游走模型的主要物理属性只是渐近定义的，因此模型识别更加复杂，因此对于短轨迹是退化的。在这里，我们引入了一种新的、快速的方法来推断基于图神经网络 (GNN) 的随机游走属性。我们的方法包括将特征向量与每个观察到的位置相关联，并将稀疏图结构与每个观察到的轨迹相关联。通过对这个结构 [1] 执行基于模拟的监督学习，我们表明我们可以可靠地学习随机游走模型及其异常指数。该方法自然可以应用于任何长度的轨迹。我们展示了它在分析 AnDi 挑战 [2] 中提出的具有生物相关性的各种异常随机游走方面的效率。我们探索了 GNN 中的信息是如何编码的，并证明它学习了随机游走的相关物理特征。我们进一步评估了它泛化到训练期间未见过的轨迹类型的能力，并且我们表明即使参数很少，GNN 也能保持高精度。