Scalable Bayesian Optimization of Composite Functions for Image-Based Inverse Problems in Materials Characterization
Dasol Yoon, Poompol Buathong, Chia-Hao Lee, Yujia Zhang, David A. Muller, Peter I. Frazier
cs.LG · cond-mat.mtrl-sci
Quick verdict
SBOCF scales composite BO to PACBED parameter fitting via 11 patch summaries, cutting synthetic SSE up to 290x but gaining only ~1.1x on experimental data.
Summary
This method paper addresses parameter estimation from PACBED (position-averaged convergent beam electron diffraction) patterns in electron microscopy, where specimen thickness and crystal mistilt are usually inferred by matching experimental images to costly multislice simulations. The authors propose SBOCF, a scalable variant of Bayesian optimization of composite functions (BOCF). Instead of modeling all 24,649 pixel intensities of a 157×157 pattern with a multi-output Gaussian process, SBOCF partitions the image into a 3×3 grid of patches, models nine patch-intensity sums plus two bounded correction terms (eleven outputs total), and propagates posterior samples through a reduced composite function that still recovers the exact pixel-wise SSE objective. Under a 50-simulation budget with a 7-point Sobol initialization and 20 repeated trials, SBOCF outperforms BO with expected improvement and knowledge gradient on synthetic SrTiO3 benchmarks: median final SSE drops by up to 290× versus BO(EI) on the thick-sample Sim380 case (47× on Sim100, 37× on Sim200). On one experimental pattern, estimates match previously reported CNN-based values, though SSE gains shrink to about 1.1× and tilt-X is slightly worse than BO(EI) (0.90×). Poisson-noise ablations show the benefit narrows at high noise, especially for thin specimens. Limitations include low dimensionality (three parameters), no ablation isolating the correction terms' contribution, and modest experimental gains. Code is public.
Review complete
Assessment at a glance
5
risk flags identified
● high 0
● medium 2
● low 3
5 strengths · 5 weaknesses · 5 author questions
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Key claims under review
- SBOCF reduces the number of modeled GP outputs from 24,649 pixel intensities to 11 (nine 3×3 patch sums plus two bounded correction terms) while preserving the exact pixel-wise SSE optimization objective.
- Under a 50-evaluation budget on synthetic SrTiO3 PACBED, SBOCF reduces median final SSE by up to 290× versus BO(EI) and 377× versus BO(KG) on the thick-sample Sim380 case.
- On the experimental Exp380 pattern, SBOCF produces thickness and mistilt estimates consistent with previously reported CNN-based values without task-specific pretraining, with modest SSE gains (1.08×/1.13×).
- SBOCF estimates on Sim200 match ground truth to within 5 Å in thickness and 0.1 mrad in tilt and recover sharp atomic columns in downstream multislice electron ptychography.
Strengths
Principled scaling of BOCF that preserves the true objective
Patch sums (Eq. 6) plus the bounded ε/δ decomposition (Eq. 8, closed form in Appendix D) let SBOCF optimize the exact pixel-wise SSE of Eq. (1) while cutting modeled GP outputs from 24,649 (157×157 pixels) to 11 — the optimization target is never silently replaced by a surrogate.
Unusually thorough evaluation protocol
20 trials with shared 7-point Sobol inits, three synthetic settings spanning thick/thin/different tilts (Sim380/Sim100/Sim200), a three-level Poisson-noise ablation (Appendix H), a partition-pattern ablation (Appendix I), per-iteration runtime reporting (Figs. 4e, 5e), and KG as a second, stronger BO baseline beyond EI.
End-to-end payoff demonstrated
Reproducibility
Honest reporting of weaker regimes
Weaknesses
Headline gains concentrated in the most favorable setting
Correction terms never ablated in isolation
Low input dimensionality limits scalability claims
Thin statistical qualification
Fixed hyperparameters and single material
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SBOCF for PACBED Parameter Estimation — Structured Preliminary Review
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Frequently asked questions
What is SBOCF and what problem does it solve?
SBOCF (scalable Bayesian optimization of composite functions) estimates physical parameters — here specimen thickness and crystal mistilt in electron microscopy — by matching an experimental PACBED diffraction image to expensive multislice simulations. It makes Bayesian optimization tractable for high-resolution images by modeling eleven quantities (nine patch-intensity sums plus two correction terms) instead of all 24,649 pixels of a 157×157 pattern, while still optimizing the exact pixel-wise sum-of-squared-errors objective.
How many simulations does SBOCF need?
In the paper, SBOCF runs within a total budget of 50 simulator evaluations, starting from a 7-point Sobol design. Under that budget it achieved lower final error than standard Bayesian optimization (expected improvement and knowledge gradient) and random sampling on synthetic SrTiO3 benchmarks; grid searches over the same thickness-tilt space would require far more simulations.
Did SBOCF work on real experimental data, not just simulations?
Yes, on one experimental SrTiO3 PACBED pattern (called Exp380, taken from a 2018 study by Xu and LeBeau). Its estimates were consistent with the previously reported CNN-based values without any task-specific pretraining. However, the gains over standard Bayesian optimization were modest there — about 1.08× in final SSE versus expected improvement — and one tilt component came out slightly worse (0.90×).
Is the code for SBOCF publicly available?
Yes. The paper states the code is available at github.com/dasol-yoon/bott, implemented in PyTorch and BoTorch, with simulations via the open-source abTEM package. Appendix E details the acquisition-function optimization settings (logEI, one-shot knowledge gradient with 16 fantasies, and 512 Sobol quasi-Monte Carlo samples for SBOCF's EI).
About this review
This is an AI-generated preliminary review by Evolve.Pub, produced from the openly available text of the paper. It is not peer review and does not represent the authors' views. The canonical record of the paper is at the publisher link above.
- Figures are extracted as text only (axis ticks and labels), so convergence curves could not be inspected directly; quantitative judgments rest on the stated median improvement factors and panel annotations rather than visual verification of the plotted trajectories.
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