KSB
TN-001 Version 1.1 Published Technical note

Technical Notes

From One-Body Representation to Interaction-Aware HAADF-STEM Surrogates

A visual technical note on the current surrogate architecture: an empirical one-body representation, interaction detection, regime selection, independent correction validation, and high-fidelity fallback.

Public supporting technical material. Scholarly status: not peer reviewed. Protected validation cases are excluded; see Scope for details.

Scope

This note explains the current research architecture using public methodology and synthetic illustrations. The original Gaussian model is shown only as a historical baseline. It does not release protected validation cases, current unpublished performance numbers, gate thresholds, or paper-critical conclusions.

Release boundary

The diagrams below describe model architecture and validation logic. They do not expose held-out validation cases, current performance values, or unpublished numerical gate thresholds.

Current scientific question

The working question is no longer whether a fixed Gaussian can approximate a STEM image. The question is when an accurate one-body representation is sufficient, when non-additive interaction becomes resolvable, and when extra model complexity is justified.

How the surrogate architecture changed

Figure 1 The fixed Gaussian is retained as a historical baseline. The current architecture first builds a phase/depth-aware empirical one-body representation, then uses an interaction gate to decide whether additive prediction, a validated correction, or high-fidelity fallback is appropriate.

The Gaussian is now a baseline

The analytical Gaussian representation remains useful as a simple historical baseline and diagnostic. It is not the current one-body surrogate. The active one-body representation is empirical and accounts for sampling phase and depth.

Historical Gaussian baseline diagnostic

Two synthetic Gaussian intensity profiles with the same centre and slightly different amplitudes and widths, used only to illustrate a historical baseline.
Figure 2 Synthetic profile comparison illustrating amplitude and width mismatch in a simple Gaussian baseline. The curves are illustrative only and are not current research measurements or the active surrogate representation.

Phase/depth-aware one-body representation

Figure 3 Conceptual atlas of empirical isolated-atom fields indexed by sampling phase and atomic depth. An unseen condition is represented by interpolation between nearby atlas entries. No protected STEM image is shown.

Validation workflow

Flow diagram from one atomic structure to an empirical one-body atlas and a multislice reference, followed by observable comparison and a validated-domain decision.
Figure 4 The same structure is evaluated by the one-body surrogate and a high-fidelity reference. Task-relevant observables are compared before deciding whether the case lies inside a validated modelling regime.

Interaction is a regime question

Figure 5 Qualitative regime map. As local geometry changes, non-additivity can be clearly resolvable, uncertain relative to numerical uncertainty, or small enough that an additive representation is adequate. Current unpublished threshold values are intentionally omitted.

Detecting interaction is not validating a correction

Figure 6 Interaction detection and correction validation are separate gates. A detectable interaction does not justify a correction unless that correction also passes independent validation; otherwise the model should abstain or return to the high-fidelity calculation.

Current validation stack

Table 1

Validation questions are separated so a lower-level pass cannot substitute for a higher-level one.
LayerQuestionRole
Numerical floor How much does the reference change under numerical refinement? Sets the nuisance scale
One-body representation Are isolated-atom fields represented accurately across relevant conditions? Establishes the additive baseline
Interaction detectability Is non-additivity distinguishable from the numerical floor? Determines whether interaction is resolvable
Correction validation Does a proposed interaction correction generalize on held-out cases? Tests whether extra complexity is usable
Decision level Does the selected model preserve the intended scientific decision? Defines task-level adequacy

Numerical uncertainty remains part of the model decision

Interaction should not be called resolvable merely because two simulated images differ. The physical non-additivity signal has to be interpreted relative to variation introduced by numerical refinement of the high-fidelity reference.

How Paper 1 and Paper 2 connect

Paper 1 establishes the interaction hierarchy: what non-additive terms appear and when pair or higher-order contributions matter. The active Paper 2 direction asks when that complexity is needed locally and whether geometry can select the appropriate modelling regime.

Public-release boundary

Table 2

Material that can be documented publicly versus material kept out of the note.
Public in this noteNot released here
Model definitions and evaluation concepts Protected validation cases
Illustrative calculations Unpublished performance measurements
Metric definitions and reporting structure Paper-critical conclusions
Reproducibility requirements Collaborator-sensitive material

References

Table 3

Background and related public work.
ReferenceLink
K. Sukuta et al., Nanocluster structure deduced from AC-STEM images coupled to theoretical modelling (2017). DOI 10.17586/2220-8054-2017-8-6-723-731
K. S. Bersha, A. Peña-Torres, and H. Jónsson, From AC-STEM Image to 3D Structure: A Systematic Analysis of Au55 nanocluster (2021 preprint). arXiv:2105.04270
C. Dwyer, Simulation of scanning transmission electron microscope images on desktop computers (2010). DOI 10.1016/j.ultramic.2009.11.009
C. Ophus, A fast image simulation algorithm for scanning transmission electron microscopy (2017). DOI 10.1186/s40679-017-0046-1