Physics-informed Bayesian optimization for quantitative high-resolution transmission electron microscopy

Abstract Quantitative high-resolution transmission electron microscopy (HRTEM) provides an indispensable means to understand structure-property relationships in atomic dimensions. Successful quantification requires reliable retrieval of essential atomic structural information despite artifacts arising from practically unavoidable imaging imperfections. Experimental observation combined with model-based iterative image simulation has enabled broad applications in quantitative structural and chemical determination of objects spanning zero to three dimensions. However, the large number of parameters involved makes the current multi-step, user-supervised iterative approach highly time-consuming, restricting its use to small sample areas and experienced users. In this work, we implement and apply a physics-informed Bayesian optimization (BO) framework to advance HRTEM quantification toward full automation and large-field-of-view analysis. Unlike conventional optimization methods, our approach adopts a stepwise strategy that fully leverages BO’s strength in handling high-dimensional parameter spaces, while its probabilistic engine efficiently refines the parameter space for rapid quantification. Using a BaTiO 3 single crystal that contains heavy, medium, and light elements as a model system, we demonstrate that the three-dimensional crystal structure can be determined from a single HRTEM image with a three- to four-order-of-magnitude improvement in time efficiency. This approach opens new avenues for fast, automated quantification over larger sample volumes and, promisingly, for in-situ applications.