Scalable Bayesian Optimization of Composite Functions for Image-Based Inverse Problems in Materials Characterization

Estimating physical parameters from scientific images is a common inverse problem in materials characterization that often relies on expensive physics-based simulations. In electron microscopy, specimen thickness and crystal mistilt are critical parameters that govern how electrons scatter through the sample, and therefore the accuracy of any atomic-scale structure recovered from it. They are commonly inferred by matching experimental position-averaged convergent-beam electron diffraction (PACBED) patterns to simulated ones, but grid searches scale poorly and neural-network methods require extensive pretraining that may not transfer to new conditions. Here, we propose scalable Bayesian optimization of composite functions (SBOCF), a simulation-efficient method that exploits the known composite structure of the image-matching objective and the intermediate information contained in simulated images. By representing PACBED images with patch-level summaries and two correction terms, SBOCF preserves the original pixel-wise objective while reducing the number of modeled outputs from 24,649 to 11. Under a budget of 50 simulator evaluations, SBOCF outperformed standard Bayesian optimization with expected improvement on synthetic SrTiO$_3$ benchmarks with thick and thin specimens, reducing the median final SSE by up to $290\times$ in the thick-sample case. On experimental data, SBOCF produced parameter estimates consistent with previously reported values without task-specific pretraining. For a simulated mistilted specimen, using the SBOCF estimates in a downstream ptychographic reconstruction recovered sharp atoms that were otherwise blurred. These results establish SBOCF as a promising approach for inverse problems involving expensive simulators and high-dimensional structured outputs.