Propagation of uncertainties and applications in numerical modeling: tutorial.

Some inputs of computational models are commonly retrieved from external sources (handbooks, articles, dedicated measurements), and therefore are subject to uncertainties. The known experimental dispersion of the inputs can be propagated through the numerical models to produce samples of outputs. The stemming propagation of uncertainties is already significant in metrology but also has applications in optimization and inverse problem resolution of the modeled physical system. Moreover, the information on uncertainties can be used to characterize and compare models, and to deduce behavior laws. This tutorial gives tools and applications of the propagation of experimental uncertainties through models. To illustrate the method and its applications, we propose to investigate the scattering of light by gold nanoparticles, which also enables the comparison of the full Mie theory and the dipole approximation. The position of the localized surface plasmon resonance and the corresponding value of the scattering efficiency are more specifically studied.