Physics-informed deep learning for stochastic particle dynamics estimation.

Single-particle tracking has enabled quantitative studies of complex systems, providing nanometer localization precision and millisecond temporal resolution in heterogeneous environments. However, at micro- or nanometer scales, probe dynamics become inherently stochastic due to Brownian motion and complex interactions, leading to varied diffusion behaviors. Typically, analysis of such trajectory data involves certain moving-window operation and assumes the existence of some pseudo-steady states, particularly when evaluating predefined parameters or specific types of diffusion modes. Here, we introduce the stochastic particle-informed neural network (SPINN), a physics-informed deep learning framework that integrates stochastic differential equations to model and infer particle diffusion dynamics. The SPINN autonomously explores parameter spaces and distinguishes between deterministic and stochastic components with single-frame resolution. Using the anomalous diffusion dataset, we validated SPINN's ability to reduce frame-to-frame variability while preserving key statistical correlations, allowing for accurate characterization of different stochastic processes. When applied to the diffusion of single gold nanorods in hydrogels, the SPINN revealed enhanced microrheological properties during hydrogel gelation and uncovered interfacial dynamics during dextran/tetra-PEG liquid-liquid phase separation. By improving the temporal resolution of stochastic dynamics, the SPINN facilitates the estimation and prediction of complex diffusion behaviors, offering insights into underlying physical mechanisms at mesoscopic scales.