# Machine Learning Analysis of Anomalous Diffusion

arXiv: https://arxiv.org/abs/2412.01393 · HTML: https://mlsanity.com/paper/2412.01393/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 182 references that are in the map.
- First posted on arXiv 2 Dec 2024.

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Large Language Models Are Zero-Shot Time Series Forecasters](https://mlsanity.com/paper/2310.07820/) (2023)
- [A Survey of Convolutional Neural Networks: Analysis, Applications, and Prospects](https://mlsanity.com/paper/2004.02806/) (2020)
- [1D Convolutional Neural Networks and Applications: A Survey](https://mlsanity.com/paper/1905.03554/) (2019)
- [Ablation Studies in Artificial Neural Networks](https://mlsanity.com/paper/1901.08644/) (2019)
- [An Overview on Data Representation Learning: From Traditional Feature Learning to Recent Deep Learning](https://mlsanity.com/paper/1611.08331/) (2016)
- [Geometric deep learning reveals the spatiotemporal fingerprint of microscopic motion](https://mlsanity.com/paper/2202.06355/) (2022)
- [Learning physical properties of anomalous random walks using graph neural networks](https://mlsanity.com/paper/2103.11738/) (2021)
- [Machine learning method for single trajectory characterization](https://mlsanity.com/paper/1903.02850/) (2019)
- [Efficient recurrent neural network methods for anomalously diffusing single particle short and noisy trajectories](https://mlsanity.com/paper/2108.02834/) (2021)
- [Unsupervised learning of anomalous diffusion data](https://mlsanity.com/paper/2108.03411/) (2021)
- [WaveNet-Based Deep Neural Networks for the Characterization of Anomalous Diffusion (WADNet)](https://mlsanity.com/paper/2106.08887/) (2021)
- [Learning minimal representations of stochastic processes with variational autoencoders](https://mlsanity.com/paper/2307.11608/) (2023)
- [Bayesian inference of scaled versus fractional Brownian motion](https://mlsanity.com/paper/2201.00654/) (2021)
- [Characterization of anomalous diffusion through convolutional transformers](https://mlsanity.com/paper/2210.04959/) (2022)
- [Extreme Learning Machine for the Characterization of Anomalous Diffusion from Single Trajectories (AnDi-ELM)](https://mlsanity.com/paper/2105.02597/) (2021)
- [Variational inference of fractional Brownian motion with linear computational complexity](https://mlsanity.com/paper/2203.07961/) (2022)
- [Preface: Characterisation of Physical Processes from Anomalous Diffusion Data](https://mlsanity.com/paper/2301.00800/) (2023)
- [Machine-Learning Solutions for the Analysis of Single-Particle Diffusion Trajectories](https://mlsanity.com/paper/2308.09414/) (2023)
- [Multifractal-spectral features enhance classification of anomalous diffusion](https://mlsanity.com/paper/2401.07646/) (2024)

## Built on by (most cited first, 3 of 3)

- [Reinforcement Learning for Active Matter](https://mlsanity.com/paper/2503.23308/) (2025)
- [ALT: A Python Package for Lightweight Feature Representation in Time Series Classification](https://mlsanity.com/paper/2504.12841/) (2025)
- [Data-Efficient Learning of Anomalous Diffusion with Wavelet Representations: Enabling Direct Learning from Experimental Trajectories](https://mlsanity.com/paper/2512.08510/) (2025)

## Abstract (arXiv)

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.