How the Plots Are Generated

The figures are generated from run-level summary tables produced after the simulation outputs have been validated and combined. Failed or unavailable rows are reported separately and are not silently interpreted as successful measurements.

Perturbation-response curves

For each attack, model, and normalized epsilon, run-level measurements are grouped across materials. The plotted line is the median, which summarizes the typical response while reducing sensitivity to catastrophic outliers. Shaded bands show the reported confidence interval or interquartile interval, depending on the figure. Epsilon is displayed on a logarithmic horizontal axis. Delta-force panels also use a logarithmic vertical scale because force changes span several orders of magnitude.

Before-and-after recovery plots

Each matched run contributes an initial measurement and a final post-relaxation measurement. The two values are connected with a dotted line, allowing the direction and magnitude of change to be read directly. Materials are ordered using their calculated metric ranks rather than their numerical identifiers.

Ranking and violin plots

Run-level measurements are grouped by model. A violin represents the distribution, the internal bar represents the interquartile range, and the central point represents the median. Models are ordered by the actual median metric value, with lower values ranked first when lower indicates better recovery. Delta-force ranking plots use a logarithmic metric axis so that one extreme model does not compress the remaining distributions.

Random-seed figures

Equivalent rows from seeds 42 through 46 are aligned by material, model, attack, epsilon, precision, and other experimental parameters. Thin lines show individual seeds, while the thick line shows the cross-seed median and the shaded region shows the interquartile range. Available matched rows are plotted even when the full experiment table is incomplete; sample counts should therefore be reported with the figure.

Precision-comparison plots

Float32 and float64 results are matched using the same model, structure, attack, and attack parameters. Each point compares the two precisions for one matched run. The dashed identity line represents perfect agreement, marginal histograms show the distributions, and the reported coefficient summarizes the strength of the relationship. Relaxation-step values must remain within the configured range of 0 to 300; larger values indicate an accumulated or stale trajectory and must be regenerated rather than clipped silently.

Immediate-response topology plots

Topology is measured immediately after perturbation and before the second relaxation. Curves summarize neighbour-edge Jaccard distance, radial distribution function distance, and coordination-number change. These measurements test whether the attack changes local connectivity before the optimizer has an opportunity to recover the structure.

Post-relaxation topology plots

The same topology metrics are recalculated after relaxation and compared with the pre-attack relaxed reference. A small immediate change followed by a small final change indicates recovery. A persistent final change indicates that the relaxation ended in a structurally different configuration.

Contour exploration plots

Contour trajectories are grouped by model, material, and contour parameter. Their force, displacement, and topology responses provide a non-adversarial reference against which the gradient-based attacks can be compared.

Supercell plots

Supercell analyses repeat the structural comparison after expanding the periodic cell. Metrics are calculated using consistent periodic-neighbour and minimum-image conventions. These plots test whether observed failure modes remain visible when the represented system size changes.