AnomalousNet: A Hybrid Approach with Attention U-Nets and Change Point Detection for Accurate Characterization of Anomalous Diffusion in Video Data

Anomalous diffusion occurs in a wide range of systems, including protein transport within cells, animal movement in complex habitats, pollutant dispersion in groundwater, and nanoparticle motion in synthetic materials. Accurately estimating the anomalous diffusion exponent and the diffusion coefficient from the particle trajectories is essential to distinguish between sub-diffusive, super-diffusive, or normal diffusion regimes. These estimates provide a deeper insight into the underlying dynamics of the system, facilitating the identification of particle behaviors and the detection of changes in diffusion states. However, analyzing short and noisy video data, which often yield incomplete and heterogeneous trajectories, poses a significant challenge for traditional statistical approaches. We introduce a data-driven method that integrates particle tracking, an attention U-Net architecture, and a change-point detection algorithm to address these issues. This approach not only infers the anomalous diffusion parameters with high accuracy but also identifies temporal transitions between different states, even in the presence of noise and limited temporal resolution. Our methodology demonstrated strong performance in the 2nd Anomalous Diffusion (AnDi) Challenge benchmark within the top submissions for video tasks.

Characterization of anomalous diffusion through convolutional transformers

The results of the Anomalous Diffusion Challenge (AnDi Challenge) have shown that machine learning methods can outperform classical statistical methodology at the characterization of anomalous diffusion in both the inference of the anomalous diffusion exponent alpha associated with each trajectory (Task 1), and the determination of the underlying diffusive regime which produced such trajectories (Task 2). Furthermore, of the five teams that finished in the top three across both tasks of the AnDi challenge, three of those teams used recurrent neural networks (RNNs). While RNNs, like the long short-term memory (LSTM) network, are effective at learning long-term dependencies in sequential data, their key disadvantage is that they must be trained sequentially. In order to facilitate training with larger data sets, by training in parallel, we propose a new transformer based neural network architecture for the characterization of anomalous diffusion. Our new architecture, the Convolutional Transformer (ConvTransformer) uses a bi-layered convolutional neural network to extract features from our diffusive trajectories that can be thought of as being words in a sentence. These features are then fed to two transformer encoding blocks that perform either regression or classification. To our knowledge, this is the first time transformers have been used for characterizing anomalous diffusion. Moreover, this may be the first time that a transformer encoding block has been used with a convolutional neural network and without the need for a transformer decoding block or positional encoding. Apart from being able to train in parallel, we show that the ConvTransformer is able to outperform the previous state of the art at determining the underlying diffusive regime in short trajectories (length 10-50 steps), which are the most important for experimental researchers.

Efficient recurrent neural network methods for anomalously diffusing single particle short and noisy trajectories

Anomalous diffusion occurs at very different scales in nature, from atomic systems to motions in cell organelles, biological tissues or ecology, and also in artificial materials, such as cement. Being able to accurately measure the anomalous exponent associated with a given particle trajectory, thus determining whether the particle subdiffuses, superdiffuses or performs normal diffusion is of key importance to understand the diffusion process. Also, it is often important to trustingly identify the model behind the trajectory, as this gives a large amount of information on the system dynamics. Both aspects are particularly difficult when the input data are short and noisy trajectories. It is even more difficult if one cannot guarantee that the trajectories output in experiments is homogeneous, hindering the statistical methods based on ensembles of trajectories. We present a data-driven method able to infer the anomalous exponent and to identify the type of anomalous diffusion process behind single, noisy and short trajectories, with good accuracy. This model was used in our participation in the Anomalous Diffusion (AnDi) Challenge. A combination of convolutional and recurrent neural networks were used to achieve state-of-the-art results when compared to methods participating in the AnDi Challenge, ranking top 4 in both classification and diffusion exponent regression.