##  [Uncertainty Propagation](/uncertainty-propagation-0) 

 Definition

Computation of how uncertainties in model inputs, parameters, or initial conditions map through a model to produce uncertainty in outputs, predictions, or quantities of interest.

 

 

 

 

 

 





## Principle

Principle

Propagate representations of input uncertainty forward through the model using appropriate techniques — Monte Carlo sampling, linearization, polynomial chaos, surrogate models — while accounting for nonlinearity, dependencies, and numerical error.

 

 

 

 

 





## Demonstration

Demonstration

Aerospace engineers run Monte Carlo samples of uncertain aerodynamic coefficients through a CFD model to obtain a distribution of lift and determine margins for control design.

 

 

 

 

## Misapplication

Misapplication

Assuming linear maps when strong nonlinearity or threshold effects exist, using too few samples, ignoring input correlations, or treating propagation as reducing epistemic uncertainty rather than quantifying its implications.

 

 

 

 

 





## Consequence

Consequence

Produces probability distributions, confidence intervals, or sensitivity information on outputs that inform safety margins, robust design, and prioritization of uncertainty reduction efforts.

 

 

 

 

## Reversal

Reversal

Inverse approaches (parameter inference or calibration) try to deduce inputs from outputs; ignoring forward propagation or reporting only single‑point outputs hides true output variability.

 

 

 

 

 





## Boundary

Boundary

Requires specified models of input uncertainty and reliable forward models; propagation does not by itself correct model form errors and may be computationally costly for high‑dimensional problems.

 

 

 

 

 





## Semantic Tension

Semantic Tension

Tension with inverse uncertainty quantification and parameter estimation; with sensitivity analysis (which may examine local derivatives rather than full output distributions).

 

 

 

 

 





## Synthesis

Synthesis

Uncertainty propagation is the forward computational mapping from uncertain inputs to uncertain outputs, yielding distributions and diagnostics that make the consequences of input uncertainty explicit for decisions.