Statistical learning of governing equations of dynamics from in-situ electron microscopy imaging data

Recent developments in (scanning) transmission electron microscopy (S)TEM have enabled in-situ investigations of nanoscale transformations. However, understanding the physical and chemical process defining matter transformations via the analysis of large-scale in-situ (S)TEM imaging data remains challenging. Here, we experimentally investigated a reaction-convection-diffusion model to track spatial-temporal patterns in (S)TEM videos of Pt nanoparticle formation and graphene contamination. Model parameters are pursued by statistical model selection algorithms that balance descriptive capability and model parsimony to aid interpretability and suppress overfitting. Besides conventional bottom-up analysis from individual entities, the integrated mathematical model based on partial differential equations (PDE) utilizing pixel level information provides complementary system status that may serve as a feedback for optimizing experiment setting.