Objective comparison of methods to decode anomalous diffusion

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.

Geometric deep learning reveals the spatiotemporal fingerprint of microscopic motion

“…In this process, trajectory linking is often just an intermediate step necessary to get meaningful information from the data, but not the end goal itself. For example, in single-molecule fluorescence microscopy, trajectory analysis is often performed to quantify dynamic parameters such as diffusion coefficients, to determine the extent of mixed diffusive behaviors (e.g., slow/fast, mobile/confined), and to classify the diffusion mode [4,5,14].…”

“…5a-e). Although these diffusion models can give rise to anomalous diffusion, in this example they are parametrized so to have the same scaling of the mean-squared displacement of Brownian motion (α = 1) [14]. Graphs are built as described above using centroid coordinates and intensity of the localized fluorescence spots as node features and the Euclidean distance between neighboring centroids as the edge feature.…”

“…Fig. 4e) since, for α = 1, all models converge to Brownian motion and fea- ture large similarities in their statistical properties, making their classification rather challenging even when linked trajectories are available [14].…”

“…However, most of these methods are specific to a given experiment or dynamic model, and often require manual tuning of parameters. The current deeplearning revolution has fostered the development of various methods for both tracking [10][11][12][13] and estimation [14]. However, deep-learningpowered approaches have so far been bound to follow the standard analysis pipeline, providing data-driven versions of conventional approaches without taking full advantage of their possibilities [13].…”

Amortised inference of fractional Brownian motion with linear computational complexity

“…However, they are generally not statistically efficient, are prone to bias when used on experimental data and their precision can be difficult to evaluate. It is worth noting the rapid progress of machine learning based approaches [32,37], which fall in the category of feature-based approaches, and which allow to learn high quality features to perform both parameter estimation and model classification. While such machine learning approaches generally outperform hand-crafted features on numerically generated data, it remains difficult to evaluate their actual performance and robustness on empirical data.…”