Objective comparison of methods to decode anomalous diffusion

Gorka Muñoz-Gil,Hélène Kabbech,Philipp G Meyer,Giorgio Volpe,Nicolás Firbas,Chang Beom Hong,Janusz Szwabiński,Patrycja Kowalek,Stefano Bò ,Aykut Argun,Artur Widera,Jean-Baptiste Masson,Miguel Ángel García-March ,Ihor Smal,Giovanni Volpe,Zihan Huang,Jae-Hyung Jeon,Erez Aghion,Hippolyte Verdier,Hanna Loch-Olszewska,Ralf Metzler,Tom Bland,Taegeun Song,Maciej Lewenstein,A Gentili ,Borja Requena,Yeongjin Kim,Michael A Lomholt,Diego Krapf,Seongyu Park,J Alberto Conejero,Samudrajit Thapa,Òscar Garibo‐I‐Orts ,Carlo Manzo

doi:10.1038/s41467-021-26320-w

Abstract

Deviations from Brownian motion leading to anomalous diffusion are found in transport dynamics from quantum physics to life sciences. The characterization of anomalous diffusion from the measurement of an individual trajectory is a challenging task, which traditionally relies on calculating the trajectory mean squared displacement. However, this approach breaks down for cases of practical interest, e.g., short or noisy trajectories, heterogeneous behaviour, or non-ergodic processes. Recently, several new approaches have been proposed, mostly building on the ongoing machine-learning revolution. To perform an objective comparison of methods, we gathered the community and organized an open competition, the Anomalous Diffusion challenge (AnDi). Participating teams applied their algorithms to a commonly-defined dataset including diverse conditions. Although no single method performed best across all scenarios, machine-learning-based approaches achieved superior performance for all tasks. The discussion of the challenge results provides practical advice for users and a benchmark for developers.

Highlights

Deviations from Brownian motion leading to anomalous diffusion are found in transport dynamics from quantum physics to life sciences
Important models for the interpretation of experimental results are continuous-time random walk (CTRW)[11], fractional Brownian motion (FBM)[12], Lévy walk (LW)[13], annealed transient time motion (ATTM)[14], and scaled Brownian motion (SBM)[15]
The challenge consisted of three tasks: Task 1 (T1) – inference of the anomalous diffusion exponent α; Task 2 (T2) – classification of the underlying diffusion model; Task 3 (T3) – trajectory segmentation (Fig. 1c and Methods, "Organization of the challenge”)

Summary

Introduction

Deviations from Brownian motion leading to anomalous diffusion are found in transport dynamics from quantum physics to life sciences. The space explored by random walkers over time is commonly measured by the mean squared displacement (MSD), which grows linearly in time for Brownian walkers (MSD ∝ t)[4] Deviations from such a linear behavior displaying an asymptotic power-law dependence (MSD ∝ tα) have been observed in several fields and are generally referred to as anomalous diffusion[4]: subdiffusion for 0 < α < 1, and superdiffusion for α > 1 (as particular cases, α = 0 corresponds to immobile trajectories, α = 1 to Brownian motion, and α = 2 to ballistic motion). The recurrent observation of anomalous diffusion has driven an important theoretical effort to understand and mathematically describe its underlying mechanisms This effort has provided a palette of microscopic models characterized by different spatial (step length) and temporal (step duration) random distributions, both with and without long-range correlations[4]. Important models for the interpretation of experimental results are continuous-time random walk (CTRW)[11], fractional Brownian motion (FBM)[12], Lévy walk (LW)[13], annealed transient time motion (ATTM)[14], and scaled Brownian motion (SBM)[15] (some sample trajectories are shown in the central panel of Fig. 1c, see Methods, "Theoretical models”)

Methods

Results

Conclusion