# WaveNet-Based Deep Neural Networks for the Characterization of Anomalous Diffusion (WADNet)

arXiv: https://arxiv.org/abs/2106.08887 · HTML: https://mlsanity.com/paper/2106.08887/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 59 references that are in the map.
- First posted on arXiv 14 Jun 2021.

## Builds on (most cited first, 11 of 11)

- [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)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (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)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [Unsupervised speech representation learning using WaveNet autoencoders](https://mlsanity.com/paper/1901.08810/) (2019)
- [Wavenet based low rate speech coding](https://mlsanity.com/paper/1712.01120/) (2017)
- [Learning physical properties of anomalous random walks using graph neural networks](https://mlsanity.com/paper/2103.11738/) (2021)
- [Extreme Learning Machine for the Characterization of Anomalous Diffusion from Single Trajectories (AnDi-ELM)](https://mlsanity.com/paper/2105.02597/) (2021)

## Built on by (most cited first, 7 of 7)

- [Unsupervised learning of anomalous diffusion data](https://mlsanity.com/paper/2108.03411/) (2021)
- [Characterization of anomalous diffusion through convolutional transformers](https://mlsanity.com/paper/2210.04959/) (2022)
- [Preface: Characterisation of Physical Processes from Anomalous Diffusion Data](https://mlsanity.com/paper/2301.00800/) (2023)
- [Machine Learning Analysis of Anomalous Diffusion](https://mlsanity.com/paper/2412.01393/) (2024)
- [Machine-Learning Solutions for the Analysis of Single-Particle Diffusion Trajectories](https://mlsanity.com/paper/2308.09414/) (2023)
- [AnomalousNet: A Hybrid Approach with Attention U-Nets and Change Point Detection for Accurate Characterization of Anomalous Diffusion in Video Data](https://mlsanity.com/paper/2504.05271/) (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)

Anomalous diffusion, which shows a deviation of transport dynamics from the framework of standard Brownian motion, is involved in the evolution of various physical, chemical, biological, and economic systems. The study of such random processes is of fundamental importance in unveiling the physical properties of random walkers and complex systems. However, classical methods to characterize anomalous diffusion are often disqualified for individual short trajectories, leading to the launch of the Anomalous Diffusion (AnDi) Challenge. This challenge aims at objectively assessing and comparing new approaches for single trajectory characterization, with respect to three different aspects: the inference of the anomalous diffusion exponent; the classification of the diffusion model; and the segmentation of trajectories. In this article, to address the inference and classification tasks in the challenge, we develop a WaveNet-based deep neural network (WADNet) by combining a modified WaveNet encoder with long short-term memory networks, without any prior knowledge of anomalous diffusion. As the performance of our model has surpassed the current 1st places in the challenge leaderboard on both two tasks for all dimensions (6 subtasks), WADNet could be the part of state-of-the-art techniques to decode the AnDi database. Our method presents a benchmark for future research, and could accelerate the development of a versatile tool for the characterization of anomalous diffusion.