Domain of Applicability
Every validated model is trustworthy only within the range of conditions it was tested against; beyond it, confidence must degrade.
Where the Model Has Earned Trust
A model is validated over the specific range of conditions the validation experiments covered, not everywhere. The domain of applicability is that range: the region of input and operating space where the model has demonstrated agreement with reality. Inside it, the model can be trusted to its validated accuracy. Outside it, every prediction is an extrapolation whose reliability is unknown and generally decreasing with distance.
Defining the Domain
- Map the conditions each validation experiment covered: geometry, regime, parameter ranges.
- The union of these regions, where the model agreed with data, is the validated domain.
- Note gaps inside the nominal range where no data exists; the domain may have holes, not just edges.
Extrapolation and Its Risks
Design points often lie partly or wholly outside the validated domain, because the whole purpose of the design may be to reach conditions no experiment has yet achieved. Predicting there is legitimate but must be labeled as extrapolation. The danger is model-form uncertainty, which is bounded only where data exists and can grow unpredictably as new physics becomes important in the untested regime. A model that fits all available data can still fail in a new one.
Managing the Gap
When a decision depends on an extrapolated prediction, the responsible responses are to widen the uncertainty to reflect the extrapolation, to add design margin, and to prioritize the experiment that would extend the domain to cover the design point. Stating the distance between the validated domain and the design point is itself important information, because it tells a reviewer how much of the prediction rests on demonstrated agreement versus on faith in the model's form.
For fusion systems aiming at conditions beyond existing devices, the honest framing is explicit: the validated domain covers what current experiments reach, and full-device performance is a projection beyond it, which is why confirming claims are reserved for the machine itself.