Semantic segmentation of anomalous diffusion using deep convolutional networks

Heterogeneous dynamics commonly emerges in anomalous diffusion with intermittent transitions of diffusion states but proves challenging to identify using conventional statistical methods. To effectively capture these transient changes of diffusion states, we propose a deep learning model (U-AnDi) for the semantic segmentation of anomalous diffusion trajectories. This model is developed with the dilated causal convolution (DCC), gated activation unit (GAU), and U-Net architecture. The study addresses two key subtasks related to trajectory segmentation and changepoint detection, concentrating on variations in diffusion exponents and dynamic models. Additionally, extended analyses are conducted on the segmentation of single-model trajectories, multistate biological trajectories, and anomalous diffusion with added correlation functions. By rationally designing comparative models and evaluating the performance of U-AnDi against these models, we discover that U-AnDi consistently outperforms other models across all segmentation tasks, thereby affirming its superiority in the field. This performance edge also sheds light on the interpretability of U-AnDi's core components: DCC, GAU, and U-Net. The clarity with which these components contribute to U-AnDi's success underscores their congruence with the intrinsic physics underlying anomalous diffusion. Furthermore, our model is examined using real-world anomalous diffusion data: the diffusion of transmembrane proteins on cell membrane surfaces, and the segmentation results are highly consistent with experimental observations. Our findings could offer a heuristic deep learning solution for the detection of heterogeneous dynamics in single-molecule/particle tracking experiments, and have the potential to be generalized as a universal scheme for time-series segmentation.