# Learning physical properties of anomalous random walks using graph neural networks

arXiv: https://arxiv.org/abs/2103.11738 · HTML: https://mlsanity.com/paper/2103.11738/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 131 references that are in the map.
- First posted on arXiv 22 Mar 2021.

## Builds on (most cited first, 21 of 21)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Differentiable Graph Module (DGM) for Graph Convolutional Networks](https://mlsanity.com/paper/2002.04999/) (2020)
- [Nonparametric Bayesian inference of the microcanonical stochastic block model](https://mlsanity.com/paper/1610.02703/) (2016)
- [A Survey on Graph Processing Accelerators: Challenges and Opportunities](https://mlsanity.com/paper/1902.10130/) (2019)
- [Construction of and efficient sampling from the simplicial configuration model](https://mlsanity.com/paper/1705.10298/) (2017)
- [Modelling Point Spread Function in Fluorescence Microscopy with a Sparse Combination of Gaussian Mixture: Trade-off between Accuracy and Efficiency](https://mlsanity.com/paper/1809.01579/) (2018)

## Built on by (most cited first, 10 of 10)

- [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)
- [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 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)
- [Representation learning for a generalized, quantitative comparison of complex model outputs](https://mlsanity.com/paper/2208.06530/) (2022)
- [Bottom-up Iterative Anomalous Diffusion Detector (BI-ADD)](https://mlsanity.com/paper/2503.11529/) (2025)
- [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)

Single particle tracking allows probing how biomolecules interact physically with their natural environments. A fundamental challenge when analysing recorded single particle trajectories is the inverse problem of inferring the physical model or class of models of the underlying random walks. Reliable inference is made difficult by the inherent stochastic nature of single particle motion, by experimental noise, and by the short duration of most experimental trajectories. Model identification is further complicated by the fact that main physical properties of random walk models are only defined asymptotically, and are thus degenerate for short trajectories. Here, we introduce a new, fast approach to inferring random walk properties based on graph neural networks (GNNs). Our approach consists in associating a vector of features with each observed position, and a sparse graph structure with each observed trajectory. By performing simulation-based supervised learning on this construct [1], we show that we can reliably learn models of random walks and their anomalous exponents. The method can naturally be applied to trajectories of any length. We show its efficiency in analysing various anomalous random walks of biological relevance that were proposed in the AnDi challenge [2]. We explore how information is encoded in the GNN, and we show that it learns relevant physical features of the random walks. We furthermore evaluate its ability to generalize to types of trajectories not seen during training, and we show that the GNN retains high accuracy even with few parameters. We finally discuss the possibility to leverage these networks to analyse experimental data.