The field of linear-elasticity, for example, is one for which there are a range of known theoretical solutions, e.g., thick cylinders subjected to internal pressure. Where known theoretical solutions are not available, e.g., the transition region between a thick cylinder and a hemispherical dome, then numerical simulation techniques, such as the finite element (FE) method might be used. The FE method, whilst generally approximate for a given mesh, has the desirable property that is converges to the theoretical solution with mesh refinement.
For the results from the type of analysis described above to be accurate requires assurance that the input parameters to the model are reliably known. This is often, even generally, not the case with reliable definitions of problem geometry, material properties and loading and boundary conditions, etc, not being available. IT is often the case, though, that these parameters are known to within some degree of accuracy or within certain prescribed bounds. A recurrent example here is whether or not to assume structural supports to be considered as fixed or simply-supported.
Uncertainty quantification considers the degree of uncertainty in the input data and assesses how it might influence the results and, therefore, the engineering decisions made from an analysis.