Estimating Computational Noise in Numerical Simulations

S. Wild (Argonne National Laboratory)

Computational noise in deterministic simulations is as ill-defined a concept as can be found in scientific computing. Roundoff errors, discretizations, numerical solutions to systems of equations, and adaptive techniques destroy the smoothness of the processes underlying the simulation. Computational noise complicates optimization, sensitivity analysis, and other applications, which depend on the simulation output. In this talk we present examples of computational noise in scientific computing and an algorithm for quantifying this noise.

Following the work of Hamming, we construct a theoretical framework for characterizing stochastic noise using only the computed function values. We present an algorithm based on this framework and show that it usually estimates the computational noise using 6 additional function evaluations. Our numerical tests suggest the algorithm is also effective for deterministic functions, and that it can be used to construct confidence intervals for functions of complex numerical simulations.

Joint work with Jorge Moré (ANL) and Julio Goez (Lehigh).