A core-design surrogate needs a mapped region of supported geometries. Check the optimizer’s preferred candidates against that region, then verify governing-model results before a prediction becomes a design choice.
Save the joint training coordinates, material categories and model versions. Individual minimum and maximum values are insufficient to describe this domain.
Check supported parameter combinations
Consider illustrative normalized training coordinates (0,0), (1,0) and (0,1). A new point (1,1) lies within each coordinate’s separate range, yet outside the triangle formed by the observations. A box test labels it “in range” while concealing the unsupported combination.
| Candidate-domain check | What it reveals | What it cannot establish |
|---|---|---|
| Individual parameter limits | Obvious coordinate extrapolation | Support for the joint combination |
| Nearest supported combinations | Distance from evaluated designs | A universal error bound |
| Material and topology category | Whether that construction was represented | Validity obtained by interpolating category labels |
| Governing-model recalculation | Surrogate discrepancy at the chosen point | Physical accuracy of the governing model |
Scale distances using meaningful design ranges or justified sensitivities. Millimetres, tesla and a dimensionless ratio cannot be placed in an unscaled Euclidean distance and expected to contribute sensibly. A categorical steel grade or duct layout needs a separate coverage check, not an arbitrary numeric spacing.
Look for sparse interiors and changed mechanisms
Even an interior point can have weak support if its nearest evaluations are distant or if a nonlinear boundary passes between them. Saturation, a layer-count change or a new duct topology can invalidate a smooth local approximation.
Plot the candidates against actual training samples in the dimensions most relevant to the limiting response. Record a domain flag with every prediction. Predicted statistical uncertainty may help select the next evaluation, but it depends on the surrogate’s assumptions and training; an apparently confident extrapolation can still be wrong. [1]
Recalculate the attractive boundary points
Run the governing model for candidates that offer a large improvement, approach a constraint or occupy poorly supported regions. Compare loss and each limiting constraint, not just the objective. A correct objective with an optimistic temperature prediction can still select an infeasible core.
If these new points are added to training, re-fit and retain separate validation cases. Repeatedly correcting the model at its current optimum can improve the search, but those points are no longer independent validation.
Assume the training library contains 900–1,100 sheets at the catalogue 0.23 mm gauge [2]: nominal steel sums span 207–253 mm. A 1,200-sheet candidate is 276 mm, 23 mm beyond that boundary. Interior interpolation residuals cannot validate it. Assume a predicted 20 W improvement and a provisional ±40 W sensitivity envelope: the possible improvement spans −20 to +60 W, so its sign is unresolved. That provisional envelope is not a validated extrapolation-error bound. Recalculate the candidate with an independently checked model, then preserve unused verification evidence before adding it to training.
Sheet count, available widths, step-lap geometry and duct choices create physical boundaries and discontinuities. Flag candidates that cross them; a smooth polynomial must not create an unavailable packet arrangement.
Report surrogate prediction, governing-model verification and physical test separately. Advance the candidate when its supported result retains the intended advantage.
References
- NIST/SEMATECH, e-Handbook of Statistical Methods, Model Validation, section 4.4.4, and Estimation, section 4.1.3.1.
- Nippon Steel Corporation, Grain-Oriented Electrical Steel Sheets, catalogue D004je, April 2020, specification and typical-property tables.