# Measurement of Anomalous Diffusion Using Recurrent Neural Networks

## TL;DR

This paper demonstrates that recurrent neural networks can accurately and efficiently characterize anomalous diffusion from limited and irregular data, outperforming traditional methods and handling complex diffusion behaviors.

## Contribution

The authors introduce a novel RNN-based approach for analyzing anomalous diffusion, capable of estimating exponents from short, irregular trajectories and identifying switching behaviors.

## Key findings

- RNN outperforms standard MSD estimation with limited data
- Method accurately estimates diffusion exponents from irregular sampling
- Successfully applied to experimental colloid and microswimmer data

## Abstract

Anomalous diffusion occurs in many physical and biological phenomena, when the growth of the mean squared displacement (MSD) with time has an exponent different from one. We show that recurrent neural networks (RNN) can efficiently characterize anomalous diffusion by determining the exponent from a single short trajectory, outperforming the standard estimation based on the MSD when the available data points are limited, as is often the case in experiments. Furthermore, the RNN can handle more complex tasks where there are no standard approaches, such as determining the anomalous diffusion exponent from a trajectory sampled at irregular times, and estimating the switching time and anomalous diffusion exponents of an intermittent system that switches between different kinds of anomalous diffusion. We validate our method on experimental data obtained from sub-diffusive colloids trapped in speckle light fields and super-diffusive microswimmers.