When Surrogates Fail

Surrogates fail silently more often than loudly; knowing the failure modes and how to detect them is as important as building the model.

Failure is the default outside the data

A surrogate interpolates its training data well and extrapolates poorly. The dangerous case is not visible error but confident error: a model that reports low uncertainty in a region it has never seen. Most surrogate failures trace to using predictions outside the region and conditions where the model was trained and validated.

Common failure modes

• Extrapolation beyond the convex hull of the training data
• Unmodeled discontinuities, thresholds, or bifurcations in the response
• Overfitting: fitting noise, giving tight but wrong predictions
• Poorly calibrated uncertainty that does not widen where it should
• Input distribution shift: the deployment inputs differ from training inputs
• Dimension mismatch: important inputs omitted or wrongly fixed

Detection

Detect failures by monitoring predictive variance for suspicious flatness far from data, by novelty or out-of-distribution detection on incoming inputs, by cross-validation residuals stratified across input space, and by spot-checking against the true model at decision-relevant points. Conformal prediction adds a coverage guarantee that flags systematic miscalibration.

Guardrails

• Refuse or flag predictions outside the training hull
• Report the distance from the nearest training point alongside each prediction
• Trigger active-learning refinement when uncertainty crosses a threshold
• Keep a validation reserve of true-model runs for periodic checks

Discipline over cleverness

The most reliable protection is procedural: define and publish the domain of validity, propagate emulator error into every reported statistic, and verify against the true model near any boundary a decision depends on. For fusion design, where the machines are simulated and not yet built, this discipline is what separates an honest gate from a persuasive but unsupported claim.