A translator at the negotiating table doesn't listen to every word; they grasp the meaning of whole phrases. Electron microscopy poses a similar challenge: you need to figure out the crystal's thickness and its tilt in the beam, and all you have is a diffraction pattern, a mosaic of thousands of bright and dark spots. Comparing every pixel of that pattern with a simulation is too costly, so researchers proposed listening not to individual words but to the meaning of fragments.

SBOCF cuts the image into nine squares, like a page into paragraphs, and for each it sums the brightness. Instead of 24,649 pixels, only 11 numbers remain: nine sums plus two correction coefficients that capture residual discrepancy. These numbers are modeled by independent Gaussian processes, cheap stand-ins for expensive simulations. Bayesian optimization, like a seasoned negotiator, picks the next thickness and tilt pair that promises the greatest improvement.

Previously, for each new material you had to either run thousands of simulations or train a neural network on a large library. SBOCF requires no training set: it uses only the structure of the objective function and a budget of 50 simulations. On experimental data, the estimated thickness and tilt agree with previously published values, and the time to choose the next point is about 0.2 minutes per iteration.

A translator who can hear the meaning of whole phrases works faster and more accurately. Likewise, SBOCF reduces the problem to 11 numbers, finds the crystal parameters in 50 simulations, and improves the subsequent reconstruction of the atomic structure. The method can already be integrated into electron microscopy workflows, and in the future it could be applied to X-ray diffraction or neutron scattering.