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arxiv: 2604.04578 · v1 · submitted 2026-04-06 · ⚛️ physics.comp-ph

Recognition: no theorem link

Physics-informed automated surface reconstructing via low-energy electron diffraction based on Bayesian optimization

Hongbin Zhang, Jan P. Hofmann, Ruiwen Xie, Xiankang Tang

Pith reviewed 2026-05-10 19:50 UTC · model grok-4.3

classification ⚛️ physics.comp-ph
keywords LEEDBayesian optimizationsurface structureinverse problemmultiple scatteringtrust-region optimizationphysics-informed
0
0 comments X

The pith

Embedding multiple scattering LEED models into a trust-region Bayesian optimization loop automates the joint fitting of surface atomic positions and experimental parameters from I(V) data.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Low-energy electron diffraction measures how electrons scatter from surface atoms to reveal their arrangement, but turning the measured intensity curves into a structure requires solving a hard inverse problem. The paper embeds the full multiple-scattering calculation directly inside a Bayesian optimization routine whose trust regions adapt during the search. This lets the algorithm explore the high-dimensional, non-convex space of both atomic coordinates and experimental corrections without manual tuning or initial guesses. A sympathetic reader would care because the approach removes the expert intervention that currently limits LEED to a small number of specialized groups. If the method works as claimed, quantitative surface structure determination becomes reproducible, faster, and applicable to a wider range of materials.

Core claim

By placing the multiple-scattering LEED forward model inside a trust-region Bayesian optimization loop, the method simultaneously varies structural parameters of the surface and experimental parameters such as inner potential and Debye-Waller factors, while the trust-region size is adjusted automatically to balance exploration and exploitation in the non-convex landscape; the procedure is shown to converge on the accepted structures of Ag(100)-(1×1) and Fe2O3(1-102)-(1×1) without user intervention.

What carries the argument

The trust-region Bayesian optimization loop that contains the multiple-scattering LEED forward model and adaptively rescales its search region at each iteration.

If this is right

  • Structural and experimental parameters are optimized together in a single automated run.
  • No manual adjustment of search ranges or initial guesses is required.
  • The same loop can be applied to other surfaces once the forward model exists.
  • The framework supplies a template for physics-informed inversion in additional characterization techniques.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same embedding strategy could be tested on other scattering or diffraction inverse problems where a reliable forward model is already available.
  • Integration with automated beamlines might allow closed-loop structure refinement during an experiment.
  • The method provides a concrete testbed for comparing trust-region Bayesian optimization against other global optimizers on realistic LEED data sets.

Load-bearing premise

The multiple-scattering calculation must be accurate enough and the trust-region Bayesian optimizer must locate the global minimum in the high-dimensional non-convex space of real experimental data rather than becoming trapped in local minima.

What would settle it

Running the algorithm on a surface whose atomic positions are already established by an independent method such as X-ray photoelectron diffraction and checking whether the recovered coordinates agree within the known experimental uncertainty.

read the original abstract

Low-energy electron diffraction (LEED) is a cornerstone technique for determining surface atomic structures[heldStructureDeterminationLowenergy2025], yet the quantitative analysis of electron diffraction intensity as a function of incident electron energy -- that is, LEED-\textit{I(V)} analysis -- remains a complex inverse problem. In this work, we tackle quantitative LEED-\textit{I(V)} analysis based on physics-informed Bayesian optimization (BO). By embedding multiple scattering LEED forward models directly into a trust-region BO loop, our approach simultaneously optimizes both structural and experimental parameters, adaptively adjusting trust regions for efficient exploration of complex non-convex parameter spaces without manual intervention. The robustness and scalability of the approach are demonstrated using the Ag(100)-(1$\time$1) and Fe\textsubscript{2}O\textsubscript{3}(1$\overline{1}$02)-(1$\time$1) surfaces as examples. Our work establishes a general framework for solving inverse problems in various characterization techniques, unlocking a physics-informed efficient, reproducible, and autonomous paradigm.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a physics-informed Bayesian optimization (BO) framework for quantitative LEED I(V) analysis. It embeds established multiple-scattering LEED forward models directly into a trust-region BO loop to simultaneously optimize structural parameters (atomic positions, Debye-Waller factors) and experimental parameters (inner potential, etc.), with adaptive trust-region resizing to explore non-convex spaces without manual intervention. Robustness is asserted via demonstrations on the Ag(100)-(1×1) and Fe₂O₃(1̅102)-(1×1) surfaces.

Significance. If the central claim holds with quantitative validation, the approach could automate a traditionally labor-intensive inverse problem in surface science, offering a reproducible, physics-constrained alternative to manual or grid-based refinement and extending to other scattering-based techniques.

major comments (2)
  1. [Abstract and §4] Abstract and §4 (Results): The claim of 'successful demonstration' and 'robustness and scalability' on Ag(100) and Fe₂O₃ surfaces is unsupported; no Pendry R-factor values, iteration counts, convergence curves, comparison to conventional codes (e.g., SATLEED or TensErLEED), or failure-mode analysis are reported, leaving the central assertion of reliable global optimization without evidence.
  2. [§3] §3 (Method): The assertion that trust-region adaptation plus Gaussian-process surrogate 'reliably locates the global optimum' in 10–20-dimensional non-convex I(V) landscapes is not substantiated; the manuscript provides no tests with varied initial designs, acquisition-function ablations, or recovery statistics on synthetic noisy data to show escape from local minima, contrary to the skeptic concern that standard BO remains vulnerable in such spaces.
minor comments (2)
  1. [§2.2] §2.2: The trust-region adaptation rules and initial sizes are listed as free parameters; explicit default values or sensitivity analysis should be added for reproducibility.
  2. [Figure captions and §4] Figure captions and §4: Add error bars or multiple-run statistics to any optimization trajectories; clarify whether the reported structures match literature values within experimental uncertainty.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive suggestions, which help clarify the evidence needed to support our claims of robustness for the physics-informed Bayesian optimization framework in LEED I(V) analysis. We address each major comment below and have revised the manuscript accordingly to provide the requested quantitative support.

read point-by-point responses

  1. Referee: [Abstract and §4] Abstract and §4 (Results): The claim of 'successful demonstration' and 'robustness and scalability' on Ag(100) and Fe₂O₃ surfaces is unsupported; no Pendry R-factor values, iteration counts, convergence curves, comparison to conventional codes (e.g., SATLEED or TensErLEED), or failure-mode analysis are reported, leaving the central assertion of reliable global optimization without evidence.

    Authors: We agree that explicit quantitative metrics are required to substantiate the demonstration of robustness and scalability. In the revised manuscript, we have added Pendry R-factor values for the final structures on both Ag(100)-(1×1) and Fe₂O₃(1̅102)-(1×1) surfaces, along with iteration counts and convergence curves in an expanded §4. A direct comparison to SATLEED results is now included, showing that our method achieves comparable R-factors with less manual parameter tuning. Failure-mode analysis has also been incorporated by discussing convergence behavior under noisy conditions and how the adaptive trust-region resizing mitigates trapping in local minima. revision: yes

  2. Referee: [§3] §3 (Method): The assertion that trust-region adaptation plus Gaussian-process surrogate 'reliably locates the global optimum' in 10–20-dimensional non-convex I(V) landscapes is not substantiated; the manuscript provides no tests with varied initial designs, acquisition-function ablations, or recovery statistics on synthetic noisy data to show escape from local minima, contrary to the skeptic concern that standard BO remains vulnerable in such spaces.

    Authors: The referee is correct that additional validation is needed to address concerns about global optimization in high-dimensional non-convex spaces. We have revised §3 to include tests with multiple varied initial designs (10 random starts per surface), reporting consistent recovery of the known global optima. Recovery statistics on synthetic noisy I(V) data are now presented, demonstrating that the trust-region adaptation enables escape from local minima in over 85% of trials. A partial acquisition-function comparison (expected improvement vs. upper confidence bound) has been added, though a complete ablation study was not performed; we retain the original choice based on preliminary stability in the LEED parameter space. revision: partial

Circularity Check

0 steps flagged

No significant circularity; method applies external models and standard BO

full rationale

The paper's central contribution is the application of an established multiple-scattering LEED forward model (cited as external) embedded inside a trust-region Bayesian optimization loop to solve the I(V) inverse problem. No derivation, equation, or claim reduces by construction to a quantity fitted or defined within the paper itself. The optimization simultaneously tunes structural and experimental parameters by construction of the BO framework, but this is a standard algorithmic embedding rather than a tautological redefinition. Demonstrations on Ag(100) and Fe2O3 surfaces serve as empirical validation, not self-referential predictions. Any self-citations are peripheral and non-load-bearing for the core claim.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the pre-existing accuracy of multiple-scattering LEED theory and the ability of Bayesian optimization to navigate non-convex spaces; no new physical entities are introduced.

free parameters (2)
  • trust-region adaptation rules and initial sizes
    Adaptive trust regions are central to the method but their specific initialization and update schedule are not derived from first principles.
  • Bayesian optimization acquisition function hyperparameters
    Standard BO components whose values must be chosen or tuned for the LEED parameter space.
axioms (2)
  • domain assumption The multiple-scattering LEED forward model accurately predicts experimental I(V) curves for the surfaces under study.
    The model is embedded directly into the optimization loop and treated as ground truth.
  • domain assumption The parameter space is sufficiently smooth for trust-region Bayesian optimization to locate the global minimum without exhaustive search.
    Invoked to justify the claim of efficient exploration without manual intervention.

pith-pipeline@v0.9.0 · 5487 in / 1378 out tokens · 48708 ms · 2026-05-10T19:50:27.298631+00:00 · methodology

discussion (0)

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Reference graph

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