Many systems in biology, physics, and finance exhibit anomalous diffusion dynamics where the mean squared displacement grows with an exponent that deviates from one. When studying time series recording the evolution of these systems, it is crucial to precisely measure the anomalous exponent and confidently identify the mechanisms responsible for anomalous diffusion. These tasks are difficult when only few short trajectories are available, a common scenario in non-equilibrium and living systems. We show that long short-time memory (LSTM) recurrent neural networks excel at characterizing anomalous diffusion from a single short trajectory. The method we developed generalizes to experimental data obtained from subdiffusive colloids trapped in speckle light fields and superdiffusive microswimmers. We discuss the performance of the method in comparison to alternative ones in the context of the Anomalous Diffusion Challenge. In closing, we address the interpretability of the method.
Anomalous diffusion occurs in many physical and biological phenomena, when the growth of the mean squared displacement with time has an exponent different from one and can be due to different mechanisms. We show that recurrent neural networks (RNNs) efficiently characterize anomalous diffusion by identifying the mechanism causing it and determining the anomalous exponent from a single short trajectory.
This method outperforms standard techniques and advanced ones when the available data points are limited, as is often the case in experiments. Furthermore, RNNs 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 measuring intermittent systems that switch between different kinds of anomalous diffusion. The method is validated on experimental data obtained from subdiffusive colloids trapped in speckle light fields and superdiffusive microswimmers.
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