Adjoint code generator

Science in China, Series F: Information Sciences

Volumn 52, Issue 6, 2009, Pages 926-941

  Cheng, Qiang ^a,b   Cao, JianWen ^c   Wang, Bin ^a   Zhang, HaiBin ^d  

^a INSTITUTE OF ATMOSPHERIC PHYSICS   (China)

^b INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

^c INSTITUTE OF SOFTWARE   (China)

^d BEIJING UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Adjoint model; Automatic differentiation; Gradient; Hessian

Indexed keywords

EID: 70349789312     PISSN: 10092757     EISSN: 18622836     Source Type: Journal    
DOI: 10.1007/s11432-009-0098-5     Document Type: Article

References (36)

1. Yamamoto T. On the method of tangent hyperbolas in Banach spaces. J Comput Appl Math, 1998, 21: 75-86.
2. Deng N Y, Zhang H B. Theoretical efficiency of a new inexact method of tangent hyperbolas. Optim Methods Softw, 2004, 19(3-4): 247-265.
3. Knoll D A, Keys D E. Jacobian-free Newton-Krylov methods: A survey of approaches and applications. J Comput Phys, 2004, 193(2): 357-397.
4. Wolfram S. The Mathematica Book. 3rd ed. Cambridge: Cambridge University Press and Wolfram Media, Inc., 1996.
5. Waterloo Maple Software, Inc. Maple V software package, 1994.
6. Macsyma Users' Guide, 1996.
7. Griewank A. On Automatic Differentiation, Mathematical Programming: Recent Developments and Applications (Amsterdam). Iri M, Tanabe K, eds. Dordrecht: Kluwer Academic Publishers, 1989. 83-108.
8. Griewank A. Evaluating Derivatives: Principles and Techniques of Automatic Differentiation. Philadelphia: SIAM, 2000.
9. Wang B, Zou X L, Zhu J, et al. Data assimilation and its applications. Proc Natl Acad Sci USA, 2000, 97: 11143-11144.
10. Zou X L, Wang B, Liu H, et al. Use of GPS/MET refraction angles in three-dimensional variational analysis. Quart J Roy Meteor Soc, 2000, 126: 3013-3040.
11. Le Dimet F X, Talagrand O. Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus, 1986, 38(A): 97-110.
12. Zhang X, Wang B. Parallel computing of a variational data assimilation model for GPS/MET observation using the raytracing method. Adv Atmos Sci, 2004, 21: 220-226.
13. Berresa S, Bulvedab R, Coronel A, et al. Numerical identification of parameters for a flocculated suspension from concentration measurements during batch centrifugation. Chem Eng J, 2005, 111: 91-103.
14. Bischof C, Pusch G, Knoesel R. Sensitivity analysis of the MM5 weather model using automatic differentiation. Comput Phys, 1996, 10: 605-612.
15. Cacui D G. Sensitivity theory for nonlinear systems, II: Extension to additional classes of responses. J Math Phys, 1981, 22(12): 2803-2812.
16. Mu M. Nonlinear singular vectors and nonlinear singular values. Sci China Ser D-Earth Sci, 2000, 43: 375-385.
17. Griewank A. An implementation of checkpointing for the reverse or adjoint model of differentiation. ACM Trans Math Softw, 1999, 26(1): 1-19.
18. Bischof C, Haghighat M R. On hierarchical differentiation. In: Berz M, Bischof C, Corliss G, et al., eds. Computational Differentiation: Techniques, Applications, and Tools. Philadelphia, PA: SIAM, 1996. 83-94.
19. Volin YM, Ostrovskill G M. Automatic computation of derivatives with the use of the multi-class differentiation techniques. Comput Math Appl, 1985, 11: 1099-1114.
20. Griewank A. Achieve logarithmic growth of temporal and spatial complexity in reverse automatic differentiation. Optim Methods Softw, 1992, 1: 35-54.
21. Bischof C, Buker H M, Hovland P, et al. Advances in Automatic Differentiation, Lecture Notes in Computational Science and Engineering. Berlin: Springer, 2008. 64.
22. Cheng Q, Zhang L B, Wang B. Model adjointization and its costs. Sci China Ser F-Inf Sci, 2004, 47(5): 587-611.
23. Cheng Q, Zhang H B, Zhao Y H. Differentiation transforming system. Nat Sci Prog, 2009, 19(3): 397-406.
24. Levine J, Mason T. Lex and Yacc. 2nd ed. Sebastopol, CA: O Reilly and Associate Inc., 1992.
25. Giering R, Kaminski T. Recipes for adjoint code construction. ACM Trans Math Softw, 1998, 24(4): 437-474.
26. Rostating N, Dalmas S, Galligo A. Automatic differentiation in Odyssee. Tellus, 1993, 45(A): 558-568.
27. Griewank A, Juedes D, Utke J. Algorithm 755: ADOL-C, a package for the automatic differentiation of algorithms written in C/C++. ACM Trans Math Softw, 1996, 22(2): 131-167.
28. Bischof C, Carle A, Corliss G, et al. ADIFOR: Generating derivative codes for Fortran programs. Scientific Program, 1992, 1(1): 11-29.
29. Griewank A. Some bounds on the complexity of gradients, Jacobians, and Hessians. In: Pardalos P M, ed. Complexity in Nonlinear Optimization. River Edge, NJ: World Scientific Publishers, 1993. 128-161.
30. Newsam G N, Ramsdell J D. Estimation of sparse Jacobian matrices. SIAM J Algebr Discrete Method, 1983, 4: 404-417.
31. Balay S, Buschelman K, Eijkhout V, et al. PETSc 2.0 users manual. Technical Report ANL-95/11-Revision 2.1.3, Argonne National Laboratory, May 2003.
32. Zou X L, Vandenberghe F, Wang B, et al. A Raytracing operator and its adjoint for the use of GPS/MET refraction angle measurements. J Geophys Res Atmos, 1999, 104(D18): 22301-22318.
33. Wang B, Ji Z Z. Construction and numerical tests for the multi-conservation difference scheme. Chin Sci Bull, 2003, 48(10): 1016-1020.
34. Wu W, Song L C, Mo Y R, et al. Xiamen-An ab initio Spin-Free Valence Bond (VB) Program. Xiamen: Xiamen University Press, 1998.
35. Song L C, Luo Y, Dong K M, et al. Paired-permanent approach for VB theory (II). Sci China Ser B-Mech, 2001, 44(6): 561-570.
36. Roberta G, Dean A M, Green W H, et al. Hydrogen abstraction rates via density functional theory. Chem Phys Lett, 1999, 312(2-4): 262-268.