Estimating Computational Noise

Computational noise in deterministic simulations is as ill-defined a concept as can be found in scientific computing. When coupled with adaptive strategies, the effects of finite precision destroy smoothness of the simulation output and complicate subsequent analysis. Following the work of Hamming on roundoff errors, we present a new algorithm, ECnoise, for quantifying the noise level of a computed function. Our theoretical framework is based on stochastic noise but does not assume a specific distribution for the noise. For the deterministic simulations considered, ECnoise produces reliable results in a few function evaluations and offers new insights into building blocks of large scale simulations.

[1]  William W. Symes,et al.  Adaptive Simulation, the Adjoint State Method, and Optimization , 2003 .

[2]  Rinker Hall Tuesdays.  THE UNIVERSITY OF FLORIDA. , 1905, Science.

[3]  Tracee Vetting Wolf,et al.  Adaptive simulation , 2006 .

[4]  Richard Barrett,et al.  Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods , 1994, Other Titles in Applied Mathematics.

[5]  Todd Munson,et al.  Benchmarking optimization software with COPS 3.0. , 2001 .

[6]  Philip E. Gill,et al.  Practical optimization , 1981 .

[7]  R. Caflisch.  Monte Carlo and quasi-Monte Carlo methods , 1998, Acta Numerica.

[8]  Richard W. Hamming,et al.  Introduction to Applied Numerical Analysis. , 1971 .

[9]  David W. Zingg,et al.  A Jacobian-free Newton-Krylov algorithm for compressible turbulent fluid flows , 2009, J. Comput. Phys..

[10]  Dominique Pelletier,et al.  On Sensitivity Analysis for Problems with Numerical Noise , 2002 .

[11]  Françoise Chaitin-Chatelin,et al.  Lectures on finite precision computations , 1996, Software, environments, tools.

[12]  P. Gill,et al.  Computing Forward-Difference Intervals for Numerical Optimization , 1983 .

[13]  J. Richard Swenson,et al.  Tests of probabilistic models for propagation of roundoff errors , 1966, CACM.

[14]  D. Keyes,et al.  Jacobian-free Newton-Krylov methods: a survey of approaches and applications , 2004 .

[15]  高等学校計算数学学報編輯委員会編.  高等学校計算数学学報 = Numerical mathematics , 1979 .

[16]  Stefan M. Wild,et al.  Estimating Derivatives of Noisy Simulations , 2012, TOMS.

[17]  Timothy A. Davis,et al.  The university of Florida sparse matrix collection , 2011, TOMS.

[18]  K. E. Vugrin.  On the Effect of Numerical Noise in Simulation-Based Optimization , 2003 .

[19]  Nicholas J. Higham,et al.  INVERSE PROBLEMS NEWSLETTER , 1991 .

[20]  Carol S. Woodward,et al.  Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers , 2020, ACM Trans. Math. Softw..