Model-Form Uncertainty
The uncertainty from the model itself being an approximation, often the largest and hardest-to-quantify error source.
When the Model Is the Problem
Every model approximates reality: it omits phenomena, uses closures, and assumes idealizations. Model-form uncertainty, also called structural or model discrepancy uncertainty, is the error that remains even with perfect inputs and perfect numerics, because the equations themselves are not exactly right. It is frequently the largest term in the total uncertainty, and the hardest to quantify.
Why It Is Hard
- It cannot be reduced by refining the mesh or measuring inputs more precisely; those address other error sources.
- It has no natural probability distribution the way a measured parameter does.
- It is only revealed by comparison to data the model was not tuned to, which may be scarce.
Ways to Estimate It
Several approaches exist, none complete. Comparing the model to validation data bounds the discrepancy in the tested regime. Comparing alternative models of the same phenomenon reveals how much the answer depends on modeling choices. Adding a discrepancy term, calibrated against data, explicitly represents the gap between model and reality, though such a term risks absorbing other errors if not handled carefully.
The Extrapolation Trap
Model-form uncertainty is dangerous precisely because it does not announce itself. A model can match all available data and still fail badly in a new regime where the omitted physics becomes important. This is why the distance between the validation regime and the design point matters so much: model-form uncertainty is bounded only where data exists, and grows in ways that are hard to predict beyond it.
Honest practice names model-form uncertainty as a line item even when it can only be bounded loosely or not at all. A UQ result that quantifies parameter and numerical uncertainty while silently omitting model form presents a precision it does not have, and is one of the most common ways credible-looking predictions go wrong.