Locate the worst-case calibration error of the probe

Determine where the worst-case magnitude error of the forward-pass probe actually occurs across PDE families, codecs, and neural-operator architectures.

Background

The probe’s worst observed multiplicative error increases as families and architectures are added: from 1.61× to 2.10× and then to 2.85×. However, the measurements use only two seeds in the relevant cells, and the uncertainty intervals are broad. The authors therefore do not establish the location of the true worst case, leaving a concrete empirical characterization problem.

References

What is established is that the point estimate went $1.61$ to $2.10$ and then did not move with a further family; it did move with a further architecture, to $2.85\times$, which Appendix~\ref{sec:arch} reports. What is not established is where the worst case actually lies, and two seeds cannot establish it.

— Lossy Compression of PDE Training Inputs: Field Reconstruction Error Does Not Order the Cost to a Trained Operator  (2610.06095 - Le, 5 Oct 2026) in Appendix, Section “How the probe’s calibration moved,” paragraph following the sixth-family result

Whether error shape predicts the size of the over-prediction was not tested; Section~\ref{sec:refuted} reports the structural explanations that were.

— Lossy Compression of PDE Training Inputs: Field Reconstruction Error Does Not Order the Cost to a Trained Operator  (2610.06095 - Le, 5 Oct 2026) in Appendix, Section “How the probe’s calibration moved,” paragraph “Error structure”

The probe under-predicts on some family-architecture pairs, and we cannot say in advance which.

— Lossy Compression of PDE Training Inputs: Field Reconstruction Error Does Not Order the Cost to a Trained Operator  (2610.06095 - Le, 5 Oct 2026) in Appendix, Section “The second predictor,” paragraph “Localising the failure”