Sensitivity — how fragile are the results to choices?

Three studies asking whether the algorithm’s output changes when the user varies something they control. These are honest-caveat pages, not demonstrations of success. The answer matters: if the results were an artefact of a specific threshold or a specific mesh, the demonstrations would not be trustworthy.

Pages

Mesh independence

The same one-parameter diffusion sweep run at three spatial mesh resolutions (\texttt{mesh\_n} \in \{15, 30, 60\}) with the tolerance tuple held fixed. The adaptive grid, the ROM accuracy, and the eigenvector subspaces are compared across resolutions. If the algorithm is discretisation-free in the intended regime, all three should agree.

Tolerance perturbation

The load-bearing caveat behind every other figure on the reference problem. Tightening the a-posteriori pruning threshold t_\pi by 20% terminates the adaptive loop one refinement level early and degrades the reduced-order-model maximum eigenvalue relative error by roughly 7×. The ROM-vs-dense equivalence demonstrated elsewhere is a property of this benchmark’s specific tolerance choice, not a robust property of the algorithm.

Knob sweep

A per-knob sensitivity study across all verdict thresholds on the one-parameter diffusion benchmark. Each threshold is swept across a range; the terminal refinement level and per-level verdict counts are recorded. The goal is to distinguish sensitivity (the output moves when a knob moves) from a bug (the output would move the same way for any threshold). No single combination reproduces every level’s counts at once.