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Second-order algorithmic differentiation by source transformation of MPI code

Published: 12 September 2010 Publication History

Abstract

A source transformation tool for algorithmic differentiation is introduced, capable of transforming MPI-enabled code into secondorder adjoint code. Our derivative code compiler (dcc) is used for the source transformation while a runtime library handles the adjoining of the MPI routines. This paper describes in detail the link between these two components in order to compute second derivatives. This process is illustrated by a simplified parallel implementation of Burgers' equation in a second-order optimization setting, for example, Newton's method.

References

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Zwillinger, D.: Handbook of Differential Equations, 3rd edn. Academic Press, Boston (1997).
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Kelley, T.: Solving nonlinear equations with Newton's method. Fundamentals of Algorithms. SIAM, Philadelphia (2003).
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Gropp, W., Lusk, E., Skjellum, A.: Using MPI: Portable Parallel Programming with the Message Passing Interface. MIT Press, Cambridge (1994).
[4]
Hannemann, R., Marquardt, W., Gendler, B., Naumann, U.: Discrete first- and second-order adjoints and automatic differentiation for the sensitivity analysis of dynamic models. In: Procedia Computer Science. Elsevier, Amsterdam (to appear, 2010).
[5]
Utke, J., Hascoët, L., Heimbach, P., Hill, C., Hovland, P., Naumann, U.: Toward Adjoinable MPI. In: Proceedings of the 23rd IEEE International Parallel & Distributed Processing Symposium, Washington, DC, USA. IEEE Computer Society Press, Los Alamitos (2009).
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Griewank, A., Walter, A.: Evaluating Derivatives. Principles and Techniques of Algorithmic Differentiation, 2nd edn. SIAM, Philadelphia (2008).
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Schanen, M., Naumann, U., Hascoët, L., Utke, J.: Interpretative adjoints for numerical simulation codes using mpi. Procedia Computer Science 1, 1819-1827 (2010); ICCS 2010.
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Utke, J., Naumann, U., Fagan, M., Tallent, N., Strout, M., Heimbach, P., Hill, C., Wunsch, C.: OpenAD/F: A modular, open-source tool for automatic differentiation of Fortran codes. ACM Transactions on Mathematical Software 34, 1-18 (2008).
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Riehme, J., Kopmann, R., Naumann, U.: Uncertainty quantification based on forward sensitivity analysis in sisyphe. In: Proceedings of ECCOMAS-CFD 2010 (to appear, 2010).

Cited By

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  • (2012)A wish list for efficient adjoints of one-sided MPI communicationProceedings of the 19th European conference on Recent Advances in the Message Passing Interface10.1007/978-3-642-33518-1_30(248-257)Online publication date: 23-Sep-2012

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Published In

cover image Guide Proceedings
EuroMPI'10: Proceedings of the 17th European MPI users' group meeting conference on Recent advances in the message passing interface
September 2010
307 pages
ISBN:3642156452
  • Editors:
  • Rainer Keller,
  • Edgar Gabriel,
  • Michael Resch,
  • Jack Dongarra

Sponsors

  • NEC
  • Microsoft: Microsoft
  • Cray
  • CISCO
  • IBM: IBM

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 12 September 2010

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View all
  • (2012)A wish list for efficient adjoints of one-sided MPI communicationProceedings of the 19th European conference on Recent Advances in the Message Passing Interface10.1007/978-3-642-33518-1_30(248-257)Online publication date: 23-Sep-2012

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