Uncertainty Quantification
A prediction without an honest error bar is only half a result; UQ is the discipline of attaching credible uncertainty to model outputs.
A Result Needs Its Uncertainty
Uncertainty quantification, or UQ, is the practice of estimating how uncertain a model's output is, given uncertainty in its inputs, its parameters, and its structure. A number reported without an uncertainty is not yet a scientific result; it gives no basis for judging whether a difference matters or a margin is safe. UQ turns a single number into a distribution.
Sources of Uncertainty
- Input and parameter uncertainty: imperfectly known coefficients and conditions.
- Numerical uncertainty: discretization and iterative error from the solver.
- Model-form uncertainty: the equations themselves being only approximate.
- Uncertainty in the data used to calibrate or validate.
How Uncertainty Is Propagated
The core task is propagation: pushing input uncertainty through the model to output uncertainty. Monte Carlo methods sample inputs from their distributions and run the model many times; surrogate-accelerated methods do this affordably when the model is expensive; and specialized techniques target rare, high-consequence tails. The output is a distribution or an interval, not a point.
The Hardest Part Is Model-Form
Input and numerical uncertainty can be estimated systematically. Model-form uncertainty, the error from the equations being wrong, is far harder, because it asks how wrong a model is in ways its own framework cannot see. It is addressed by comparing competing models, by validation against data, and by honest acknowledgment of assumptions, never fully eliminated.
At Kronos
Design results carry input uncertainty through to output uncertainty rather than reporting a single clean figure, and conditions and assumptions are stated so model-form limits are visible. Reporting a range with its basis, instead of a bare number, is what lets a simulation-based claim be weighed honestly.