Verification, Validation, and UQ

Verification asks whether the equations are solved right, validation whether the right equations were solved, and UQ bounds the remaining confidence.

Three distinct questions

Credible computational prediction rests on three activities that are often confused. Verification checks that the equations are solved correctly - the code and its numerics. Validation checks that the equations describe reality - the model against experiment. Uncertainty quantification bounds the confidence in the resulting prediction. Together they are abbreviated VVUQ.

Verification

Verification is a mathematics and software question with no reference to the real world. Code verification confirms the software solves the equations as intended, often against analytic or manufactured solutions. Solution verification estimates the numerical error of a specific run - discretization, iteration, and round-off error - typically via mesh and time-step convergence studies.

Validation

Validation is a physics question. It compares model predictions to experimental measurements over a defined domain of applicability, accounting for uncertainty on both sides. A model validated in one regime is not automatically valid in another; the domain of validation must be stated. Validation exposes model-form error that verification cannot see.

Uncertainty quantification

• Propagate input uncertainties to bound prediction spread
• Include numerical error from solution verification
• Include model-form uncertainty from validation discrepancy
• Report a total predictive uncertainty with its assumptions

Prediction beyond the data

The hardest case is predicting where no validation data exist - the reason simulations are run at all. This requires extrapolating validated model-form uncertainty into the prediction regime, a step that must be done cautiously and stated openly. Overreaching here is how confident predictions turn out wrong.

In Kronos practice

VVUQ discipline governs modeling of the machines: numerical error is verified by convergence studies, models are validated against available experimental and published data within stated domains, and uncertainty is propagated and reported with its assumptions. Predictions outside the validated domain are labeled as such, and no simulated result is presented as a measured demonstration.