Uncertainty Quantification Overview
Uncertainty quantification turns a single model prediction into a distribution, tracing how input, model, and data uncertainties shape the answer.
Why a point answer is not enough
A simulation that reports one number hides how much that number could change if inputs, model choices, or data were slightly different. Uncertainty quantification (UQ) is the discipline of characterizing, propagating, and reducing uncertainty so predictions come with defensible error bars and so decisions account for what is unknown.
Sources of uncertainty
- Parametric - uncertain input values such as material properties or reaction rates
- Model-form - the equations themselves are approximate
- Numerical - discretization, truncation, and solver tolerance error
- Data - measurement noise and limited observations
- Aleatoric - irreducible variability in the system itself
The two directions
Forward UQ pushes known input uncertainties through the model to find the output distribution. Inverse UQ uses observed data to infer uncertain inputs or parameters, typically in a Bayesian framework. A full study often does inverse UQ to calibrate a model, then forward UQ to make predictions with the calibrated uncertainties.
Core tools
Monte Carlo and quasi-Monte Carlo sampling, polynomial chaos expansions, Gaussian-process emulators, and multilevel methods propagate uncertainty. Sensitivity analysis, especially Sobol indices, apportions output variance among inputs. Bayesian inference calibrates parameters and quantifies epistemic uncertainty. Surrogates make all of these affordable for expensive models.
The role of surrogates
Rigorous UQ can demand thousands to millions of model evaluations - impossible with an hours-long simulation. Surrogates stand in for the expensive model so the sampling completes in reasonable time. The surrogate's own approximation error then becomes another uncertainty source that must be accounted for, not ignored.
Honest UQ in practice
Credible UQ states its assumptions, separates what is reducible from what is not, and validates its uncertainty estimates against reality. In Kronos design, UQ propagates uncertainty in physics parameters through models of the machines, distinguishing what more data could tighten from what is inherent, and never presents a simulated prediction as a measured result.