Physics-informed Generative models for learning the stochastic diffusion of single particle trajectories

Interpreting the underlying physics of single particle trajectories has traditionally been approached with canonical statistical methods such as time-averaged mean squared displacement; however, these methods fail on single short trajectories, especially the ones with non-gaussian and nonergodic characteristics. These challenges have led to a body of computational research on classifying short single-particle trajectories into ideal classes of anomalous diffusion and determining their anomalous exponents using supervised and unsupervised machine learning methods. However, experimental data from single particle tracking experiments remains a largely unknown mixture of different anomalous diffusion classes with unknown anomalous exponents, making it difficult to classify them into ideal stochastic models. Here, we have developed a physics-informed generative neural network model trained on a large data set of single particle trajectories of surface diffusion of gold nanorods in aqueous solutions. We show that this model learns the time-dependent dynamics of the experimental trajectories in its continuous latent space representation based on statistical/physical properties. We demonstrate that our model can distinguish various levels of anomaly regardless of the underlying class of diffusion.