JAMES M. HYMAN
Theoretical Division and CNLS
Los Alamos National Laboratory, MS B284
Los Alamos, NM 87545, USA
hyman@lanl.gov
Abstract:
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.