Los Alamos National Laboratory
Quantifying the uncertainties in mathematical models in essential for making reliable predictions of complex phenomena. Well informed decisions based on simulations require that we can identify the significance of the inherent variability of the physical system, the impact of the approximations made in formulating the model problem, the consequences of simulation errors when solving the approximate model, the sensitivity of the prediction to our limited knowledge of the state of the system and the probabilistic implications of the inherent stochastic effects that exist in most physical systems. The magnitude of computational uncertainties is of great concern to anyone solving a complex problem, since no computation can be complete without some knowledge of its accuracy.
I will discuss the importance of quantifying these uncertainties and describe some new approaches for estimating their impact on the numerical solution of partial differential equations. The examples will illustrate how the uncertainties in a simulation can grow or even shrink during the calculation and affect the reliability of the results in unanticipated ways.