Consistent uncertainty reduction in modeling nonlinear systems

SIAM Journal on Scientific Computing

Volumn 26, Issue 2, 2005, Pages 653-665

  Barhen, Jacob ^a   Protopopescu, Vladimir ^a   Reister, David B ^a  

^a OAK RIDGE NATIONAL LABORATORY   (United States)

Author keywords

Automated differentiation; Nonlinear systems; Sensitivity analysis; Uncertainty reduction

Indexed keywords

CODES (SYMBOLS); DIFFERENTIATION (CALCULUS); MATHEMATICAL MODELS; MATRIX ALGEBRA; PARAMETER ESTIMATION; SENSITIVITY ANALYSIS; UNCERTAIN SYSTEMS;

ATMOSPHERIC CODES; AUTOMATED DIFFERENTIATION; MODELING PROCESS; UNCERTAINTY REDUCTIONS;

NONLINEAR SYSTEMS;

EID: 16244363057     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827503427522     Document Type: Article

References (41)

1. R. TOMOVIC, Sensitivity Analysis of Dynamic Systems, McGraw-Hill, New York, 1963.
2. R. TOMOVIC AND M. VUCOBRATOVIC, General Sensitivity Theory, Elsevier, New York, 1972.
3. E. M. OBLOW, Sensitivity theory from a differential viewpoint, Nuclear Sci. Engrg., 59 (1976), pp. 187-189.
4. P. FRANK, Introduction to System Sensitivity Theory, Academic Press, New York, 1978.
5. E. M. OBLOW, Sensitivity theory for general nonlinear algebraic equations, Nuclear Sci. Engrg., 65 (1978), pp. 187-191.
6. D. CACUCI, Sensitivity theory for nonlinear systems: I. Nonlinear functional analysis approach, J. Math. Phys., 22 (1981), pp. 2794-2802.
7. E. M. OBLOW AND F. G. PEREY, Screening sensitivity theory, Nuclear Sci. Engrg., 87 (1984), pp. 444-453.
8. D. G. CACUCI, Sensitivity and Uncertainty Analysis, Vol. I, Chapman & Hall/CRC, Boca Raton, FL, 2003.
9. J. LEWINS AND M. BECKER, EDS., Sensitivity and Uncertainty Analysis of Reactor Performance Parameters, Adv. Nuclear Sc. Tech. 14, Plenum Press, New York, 1982.
10. E. GREENSPAN, M. WILLIAMS, AND J. H. MARABLE, Time-dependent generalized perturbation theory for coupled neutron-nuclide problems, Nuclear Sc. Engrg., 73 (1979), pp. 210-218.
11. E. M. OBLOW, Sensitivity theory for reactor thermal hydraulics problems, Nuclear Sc. Engrg., 68 (1978), pp. 322-337.
12. D. G. CACUCI, C. F. WEBER, E. M. OBLOW, AND J. H. MARABLE, Sensitivity theory for general systems of non-linear equations, Nuclear Sc. Engrg., 75 (1980), pp. 88-110.
13. R. G. ALSMILLER, J. BARHEN, AND J. HORWEDEL, The application of adjoint sensitivity theory to a liquid fuels supply model, Energy, 9 (1984), pp. 239-253.
14. J. TOLMA AND P. BARTON, On computational differentiation, Comput. Chem. Engrg., 22 (1998), pp. 475-490.
15. A. GRIEWANK, Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, SIAM, Philadelphia, 2000.
16. E. OBLOW, An Automated Procedure for Sensitivity Analysis Using Computer Calculus, ORNL/TM-8776, Oak Ridge National Laboratory, Oak Ridge, TN, 1983.
17. E. OBLOW, GRESS: Gradient-Enhanced Software System Version B User Guide, ORNL/TM8339, Oak Ridge National Laboratory, Oak Ridge, TN, 1983.
18. E. OBLOW, Sensitivity analysis using computer calculus: A nuclear waste isolation application, Nuclear Sci. Engrg., 94 (1986), pp. 46-65.
19. C. BISCHOF, P. KHADEMI, A. MAUER, AND A. CARLE, Adifor2.0: Automatic differentiation of Fortran 77 Programs, IEEE Comput. Sci. Engrg., 3 (1996), pp. 18-32.
20. G. CORLISS, C. FAURE, A. GRIEWANK, L. HASCOET, AND U. NAUMANN, Automatic Differentiation of Algorithms: From Simulation to Optimization, Springer-Verlag, New York, 2002.
21. J. BARHEN AND D. REISTER, Uncertainty analysis based on sensitivities generated using automated differentiation, in Proceedings of the International Conference on Computational Science and Its Applications, Lecture Notes in Comput. Sci. 2668, Springer-Verlag, Berlin, 2003. pp. 70-77.
22. A. BERK, L. S. BERNSTEIN, G. P. ANDERSON, P. K. ACHARYA, D. C. ROBERTSON, J. H. CHET-WYND, AND S. M. ADLER-GOLDEN, MODTRAN cloud and multiple scattering upgrades with application to AVIRIS, Remote Sensing of Environment, 65 (1998), pp. 367-375.
23. J. BARHEN, D. G. CACUCI, J. J. WAGSCHAL, M. A. BJERKE, AND C. B. MULLINS, Uncertainty analysis of time-dependent nonlinear systems, Nuclear Sci. Engrg., 81 (1982), pp. 23-44.
24. J. BARHEN, N. TOOMARIAN, AND S. GULATI, Applications of adjoint operators to neural networks, Appl. Math. Lett., 3 (1990), pp. 13-18.
25. N. TOOMARIAN AND J. BARHEN, Neural Network Training by Integration of Adjoint Systems of Equations Forward in Time, U.S. Patent 5,930,781, July 27, 1999.
26. B. AYYUB AND M. GUPTA, Uncertainty Analysis in Engineering Sciences, Kluwer Academic, Dordrecht, The Netherlands, 1997.
27. R. MYERS, Response Surface Methodology, Allyn and Bacon, Boston, 1971.
28. R. MYERS AND D. MONTGOMERY, Response Surface Methodology, 2nd ed., John Wiley, New York, 2001.
29. N. Cox, Comparison of two uncertainty analysis methods, Nuclear Sci. Engrg., 64 (1977), pp. 258-265.
30. F. PUKELSHEIM, Optimal Design of Experiments, John Wiley, New York, 1993.
31. B. KOSKO, Fuzzy Engineering, Prentice-Hall, Upper Saddle River, NJ, 1996.
32. P. WASSERMAN, Advanced Methods in Neural Computing, Van Nostrand-Reinhold, New York, 1993.
33. M. BISHOP, Neural Networks for Pattern Recognition, Oxford University Press, Oxford, 1997.
34. F. AMINZADEH, J. BARHEN, C. GLOVER, AND N. TOOMARIAN, Estimation of reservoir parameters using a hybrid neural network, J. Petroleum Sci. Engrg., 24 (1999), pp. 49-56.
35. J. BARHEN AND D. G. CACUCI, An efficient procedure to evaluate second-order sensitivities for nonlinear problems with nonlinear responses, Trans. Amer. Nuclear Soc., 35 (1980), pp. 266-267.
36. R. DUDA, P. HART, AND D. STORK, Pattern Classification, 2nd ed., Wiley-Interscience, Chichester, UK, 2001.
37. J. BARHEN, J. J. WAGSCHAL, AND Y. YEIVIN, Lagrange multipliers in data adjustment with response-parameter correlations, Trans. Amer. Nuclear Soc., 35 (1980), pp. 246-247.
38. L. DEVROYE, L. GYÖRFI, AND G. LUGOSI, A Probabilistic Theory of Pattern Recognition, Springer-Verlag, New York, 1996.
39. T. KATO, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1984.
40. J. WAGSCHAL AND Y. YEVIN, A note on how to iterate adjustment, J. Nuclear Sci. Tech., 2 (2002), pp. 896-899.
41. A. BERK, G. P. ANDERSON, L. S. BERNSTEIN, P. K. ACHARYA, H. DOTHE, M. W. MATTHEW, S. M. ADLER-GOLDEN, J. H. CHETWYND, JR., S. C. RICHTSMEIER, B. PUKALL, C. L. ALLRED, L. S. JEONG, AND M. L. HOKE, MODTRAN4 radiative transfer modeling for atmospheric correction, in Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research III, SPIE 3756, SPIE Press, Bellingham, WA, 1999.