Machine Learning Analysis of Anomalous Diffusion

TL;DR

This paper surveys the integration of machine learning with anomalous diffusion analysis, emphasizing two core avenues: single-trajectory characterization (parameter inference and segmentation) and representation learning (predefined feature-based fingerprints, penultimate-layer embeddings, and autoencoder latent representations). It contrasts classical ML with deep learning, illustrates diverse architectures (CNNs, RNNs, GNNs), and discusses benchmarking through the AnDi Challenge, including its emphasis on segmentation in the 2024 version. The work highlights the strengths and limitations of each representation strategy, demonstrates how learned representations can generalize across models and conditions, and advocates a move toward open datasets, richer simulators, and hybrid, interpretable approaches. Collectively, the review maps a roadmap for applying AI to statistical physics and biophysics, with practical impact on accurately decoding diffusion mechanisms in complex systems.

Abstract

The rapid advancements in machine learning have made its application to anomalous diffusion analysis both essential and inevitable. This review systematically introduces the integration of machine learning techniques for enhanced analysis of anomalous diffusion, focusing on two pivotal aspects: single trajectory characterization via machine learning and representation learning of anomalous diffusion. We extensively compare various machine learning methods, including both classical machine learning and deep learning, used for the inference of diffusion parameters and trajectory segmentation. Additionally, platforms such as the Anomalous Diffusion Challenge that serve as benchmarks for evaluating these methods are highlighted. On the other hand, we outline three primary strategies for representing anomalous diffusion: the combination of predefined features, the feature vector from the penultimate layer of neural network, and the latent representation from the autoencoder, analyzing their applicability across various scenarios. This investigation paves the way for future research, offering valuable perspectives that can further enrich the study of anomalous diffusion and advance the application of artificial intelligence in statistical physics and biophysics.

Figures (10)

• Figure 1: (a) Illustrative images demonstrate anomalous diffusion across various length scales (top panel), and different dimensions (bottom panel), from Munoz2021; (b) Enhanced heterogeneous diffusion can be identified for nanoparticles in a semiflexible polymer network, from Xu2021Dai2022; (c) Intracellular transport dynamics in early apoptotic cells, where trajectories of endocytic vesicles display typical anomalous diffusion properties, from Zhang2021; (d) GPS-tracking movement data of springboks in Namibia during the wet season (top) and the dry season (bottom), both showing non-standard movement patterns on a large scale, from Meyer2023.
• Figure 2: (a) Schematic flowchart of the feature-based methods: a set of features is extracted from raw trajectories and used as the input for feature-based machine learning models, from Seckler2023; (b) A workflow of random forest algorithm for the single trajectory characterization tasks, from Munoz-Gil2; (c) Schematic of the architecture of ELM (top), and corresponding performance in classifying diffusion models (bottom), from Manzo2021.
• Figure 3: (a) Schematic diagrams of single trajectory characterizations using CNNs, from Granik2019AL-hada2022; (b) The workflow (top) and model performance (bottom) of RANDI model, which has a dual-layer LSTM structure, from Argun2021; (c) Workflow (left) and performance analysis (right) of WADNet, which is combined by a WaveNet encoder and a 3-layer LSTM network, from Li2021.
• Figure 4: (a) Representative example of graphs associated with a short diffusion trajectory, from Verdier2021; (b) Workflow of the GNN for processing diffusion trajectories, from Verdier2021; (c) Schematic diagram showing the spatiotemporal graph representation of trajectories using MAGIK, from Pineda2023; (d) Comparative analysis of trajectory linking results using MAGIK on HeLa cell video data with ground truth trajectories, from Pineda2023.
• Figure 5: (a) Illustration of three segmentation steps in the DC-MSS algorithm, from Vega2018; (b) The combination of sliding window method and BPNN for trajectory segmentation (top) and corresponding performance analysis (bottom) , from Dosset2016; (c) Workflow of Deep-SEES for trajectory segmentation where the sliding window and LSTM-VAE network are utilized, from Zhang2023.