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 SrTiO3 benchmarks with thick and thin specimens, reducing the median final SSE by up to 290x 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.

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