Application of Automatic Differentiation to Reservoir Design Models
Publication: Journal of Water Resources Planning and Management
Volume 124, Issue 3
Abstract
Automatic differentiation is a technique for computing derivatives accurately and efficiently with minimal human effort. The calculation of derivatives of numerical models is necessary for gradient-based optimization of reservoir systems to determine optimal sizes for reservoirs. The writers report on the use of automatic differentiation and divided difference approaches for computing derivatives for a single- and multiple-reservoir yield model. In the experiments, the ADIFOR (Automatic Differentiation of Fortran) tool is employed. The results show that, for both the single- and the multiple-reservoir model, automatic differentiation computes derivatives exactly and more efficiently than the divided difference implementation. Postoptimization of the ADIFOR-generated derivative code by exploiting the model structure is also discussed. The writers observe that the availability of exact derivatives significantly benefits the convergence of the optimization algorithm: the solution of the multireservoir problem, which took 10.5 hours with divided difference derivatives, is decreased to less than two hours with ADIFOR “out of the box” derivatives, and to less than an hour using the postoptimized ADIFOR derivative code.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Berz, M., Bischof, C., Corliss, G., and Griewank, A., eds. (1996). Computational differentiation—techniques, tools, and applications. Society for Industrial and Applied Mathematics, Philadelphia, Pa.
2.
Bischof, C., Carle, A., Corliss, G., Griewank, A., and Hovland, P.(1992). “ADIFOR—generating derivative codes from FORTRAN programs.”Scientific Programming, 1(1), 11–29.
3.
Bischof, C., Carle, A., Khademi, P., and Mauer, A.(1996a). “The ADIFOR 2.0 system for the automatic differentiation of FORTRAN 77 programs.”IEEE Computational Sci. & Engrg., 3(3), 18–32.
4.
Bischof, C., Corliss, G., Green, L., Griewank, A., Haigler, K., and Newman, P.(1993). “Automatic differentiation of advanced CFD codes for multidisciplinary design.”J. on Computing Sys. in Engrg., 3(5), 625–638.
5.
Bischof, C., Green, L., Haigler, K., and Knauff, T. (1994a). “Parallel calculation of sensitivity derivatives for aircraft design using automatic differentiation.”Proc., 5th AIAA/NASA/USAF/ISSMO Symp. on Multidisciplinary Anal. and Optimization, AIAA Paper 94-4261, American Institute of Aeronautics and Astronautics. Reston, Va.
6.
Bischof, C., Jones, W. T., Mauer, A., Samareh, J., and Mauer, A. (1996b). “Experiences with the application of the ADIC automatic differentiation tool to the CSCMDO 3-D volume and generation code.”Proc., 34th AIAA Aerosp. Sci. Meeting, AIAA Paper 96-0716, American Institute of Aeronautics and Astronomics, Reston, Va.
7.
Bischof, C., Roh, L., and Mauer, A. (1996c). “ADIC—an extensible automatic differentiation tool for ANSI-C.”Preprint ANL/MCS-P626-1196, Argonne National Laboratory, Argonne, Ill.
8.
Bischof, C., Whiffen, G., Shoemaker, C., Carle, A., and Ross, A. (1994b). “Application of automatic differentiation to groundwater transport models.”Computational methods in water resources X, A. Peters, ed., Kluwer, Dordrecht, The Netherlands, 173–182.
9.
Gill, P. E., Murray, W., and Wright, M. H. (1981). Practical optimization. Academic Press, New York, N.Y.
10.
Griewank, A. (1989). “On automatic differentiation.”Mathematical programming: recent developments and applications, A. L. Norwell, ed., Kluwer Academic Publishers Group, Boston, Mass., 83–108.
11.
Griewank, A., and Corliss, G. F., eds. (1991). Automatic differentiation of algorithms: theory, implementation, and application. Society of Industrial and Applied Mathematics, Philadelphia, Pa.
12.
Griewank, A., Juedes, D., and Utke, J.(1996). “ADOL-C: a package for the automatic differentiation of algorithms written in C/C++.”ACM Trans. on Mathematical Software, 22(2), 131–167.
13.
Heidari, M., and Moench, A.(1997). “Evaluation of unconfined-acquifer parameters from pumping test data by nonlinear least squares.”J. Hydro., Amsterdam, The Netherlands, 192, 300–313.
14.
Khaliquzzaman, and Chander(1997). “Network flow programming model for multireservoir sizing.”J. Water Resour. Plng. and Mgmt., ASCE, 123(1), 15–22.
15.
Lall, U.(1995). “A yield model for screening surface and ground water development.”J. Water Resour. Plng. and Mgmt., ASCE, 121(1), 9–22.
16.
Lall, U., and Miller, C. W.(1988). “An optimization model for screening multipurpose reservoir systems.”Water Resour. Res., 24(6), 953–968.
17.
Loucks, D. P., Stedinger, J. R., and Haith, D. A. (1981). Water resources systems planning and analysis. Prentice-Hall, Inc., Englewood Cliffs, N.J.
18.
Rostaing, N., Dalmas, S., and Galligo, A. (1993). “Automatic differentiation in ODYSSEE.”Tellus, 45a(4), 558–568.
19.
Shiriaev, D., and Griewank, A. (1996). “ADOL-F: Automatic differentiation of FORTRAN codes.”Computational differentiation–techniques, tools, and applications, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 375–384.
20.
Sinha, A. K., and Rao, B. V. (1996). “An optimization model for screening multipurpose reservoir systems with explicit yield reliability considerations.”Proc., Int. Conf. on Hydrology & Water Resour., V. P. Singh and B. Kumar, eds., Vol. 4, Kluwer, Dordrecht, The Netherlands.
21.
Sinha, A. K., Rao, B. V., and Lall, U. (1996). “A yield model for screening multipurpose reservoir systems.”Tech. Rep., Indian Institute of Technology, Bombay, India.
22.
Stedinger, J. R., Sule, B. F., and Pei, D.(1983). “Multiple reservoir system screening models.”Water Resour. Res., 19(6), 1383–1393.
23.
Zhou, J. L., and Tits, A. L. (1992). User's guide for FSQP. Version 3.1, Systems Research Centre, University Maryland, College Park, Md.
Information & Authors
Information
Published In
Journal of Water Resources Planning and Management
Volume 124 • Issue 3 • May 1998
Pages: 162 - 167
Copyright
Copyright © 1998 American Society of Civil Engineers.
History
Published online: May 1, 1998
Published in print: May 1998
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.