skip to main content
article
Free Access

PYTHIA: a knowledge-based system to select scientific algorithms

Published:01 December 1996Publication History
Skip Abstract Section

Abstract

Problem-solving e*nvironments (PSEs) interact with the user in a language “natural” to the associated discipline, and they provide a high-level abstraction of the underlying, computationally complex model. The knowledge-based system PYTHIA addresses the problem of (parameter, algorithm) pair selection within a scientific computing domain assuming some minimum user-specified computational objectives and some characteristics of the given problem. PYTHIA's framework and methodology are general and applicable to any class of scientific problems and solvers. PYTHIA is applied in the context of Parallel ELLPACK where there are many alternatives for the numerical solution of elliptic partial differential equations (PDEs). PYTHIA matches the characteristics of the given problem with those of PDEs in an existing problem population and then uses performance profiles of the various solvers to select the appropriate method given user-specified error and solution time bounds. The profiles are automatically generated for each solver of the Parallel ELLPACK library.—Authors' Abstract

References

  1. BAREISS, R. 1986. Exemplar-Based Knowledge Analysis. Academic Press, New York.Google ScholarGoogle Scholar
  2. BOISVERT, R. F., RICE, J. R., AND HOUSTIS, E.N. 1979. A system for performance evaluation of partial differential equations software. IEEE Trans. Softw. Eng. SE-5, 4, 418-425.Google ScholarGoogle Scholar
  3. CARPENTER, G. A. AND GROSSBERG, S. 1988. The art of adaptive pattern recognition by a self-organizing neural network. Computer 21, 77-88. Google ScholarGoogle Scholar
  4. DURBIN, R. AND WILLSttAW, D. 1987. An analogue approach to the travelling salesman problem using an elastic net method. Nature 326, 689-691.Google ScholarGoogle Scholar
  5. DYKSEN, W. R., AND GRITTER, C. R. 1989. Elliptic expert: An expert system for elliptic partial differential equations. Math. Comput. Simul. 31, 333-343.Google ScholarGoogle Scholar
  6. DYKSEN, W. R. AND GRITTER, C.R. 1992. Scientific computing and the algorithm selection problem. In Expert Systems for Scientific Computing, E. N. Houstis, J. R. Rice, and R. Vichnevetsky, Eds. North-Holland, Amsterdam, 19-31.Google ScholarGoogle Scholar
  7. DYKSEN, W. R., RIBBENS, C. J., AND RICE, J.R. 1988. The performance of numerical methods for elliptic problems with mixed boundary conditions. Num. Meth. Partial Differential Equations 4, 347-361.Google ScholarGoogle Scholar
  8. GALLOPOULOS, E., HOUSTIS, E. N., AND RICE, J.R. 1994. Problem-solving environments for computational science. IEEE Comput. Sci. Eng. 1, 11-23. Google ScholarGoogle Scholar
  9. GIARRATANO, J. C. 1991. CLIPS User's Guide. Ver. 5.1. NASA Lyndon B. Johnson Space Center, Houston, Tex.Google ScholarGoogle Scholar
  10. HOLLANDER, M. AND WOLFE, D. 1973. Nonparametric Statistical Methods. John Wiley and Sons, New York.Google ScholarGoogle Scholar
  11. HOPFIELD, J. J. AND TANK, D. 1986. Computing with neural circuits. Science 233, 625-633.Google ScholarGoogle Scholar
  12. HOUSTIS, E. N. AND RICE, J. R. 1982. High order methods for elliptic partial differential equations with singularities. Int. J. Num. Meth. Eng. 18, 737-754.Google ScholarGoogle Scholar
  13. HOUSTIS, E. N., RICE, J. R., C~RISOC~OIDES, N. P., KARATItANASIS, H. C., PAPACHIOU, P. N., SAMARTZIS, M. K., VAVALIS, E. A., WANG, K. Y., AND WEERAWARANA, S. 1990. //ELLPACK: A numerical simulation programming environment for parallel MIMD machines. In Proceedings of Supercomputing '90. ACM Press, New York, 96-107. Google ScholarGoogle Scholar
  14. HOUSTIS, E. N., RICE, J. R., CHRISTARA, C. C., AND VAVALIS, E.A. 1988. Performance of scientific software. In Mathematical Aspects of Scientific Software, J. R. Rice, Ed. Springer- Verlag, Berlin, 123-155. Google ScholarGoogle Scholar
  15. JOSHI, A., WEERAWARANA, S., AND HOUSTIS, E. N. 1994. The use of neural networks to support "intelligent" scientific computing. In Proceedings of the International Conference on Neural Networks, World Congress on Computational Intelligence. Vol. IV. 411-416.Google ScholarGoogle Scholar
  16. JOSHI, A., WEERAWARANA, S., RAMAKRISHNAN, N., HOUSTIS, E., AND RICE, J. 1996. Neurofuzzy support for problem solving environments. IEEE Comput. Sci. Eng. 3. Google ScholarGoogle Scholar
  17. KAMEL, M. S., MA, K. S., AND ENRIGHT, W.H. 1993. ODEXPERT: An expert system to select numerical solvers for initial value ODE systems. ACM Trans. Math. Softw. 19, I (Mar.), 44-62. Google ScholarGoogle Scholar
  18. KONIG, S. AND ULLRICH, C. 1990. An expert system for the economical application of self-validating methods for linear equations. In Intelligent Mathematical Software Systems, E. N. Houstis, J. R. Rice, and R. Vichnevetsky, Eds. North-Holland, Amsterdam, 195-220.Google ScholarGoogle Scholar
  19. MOORE, P. K., OZTURAN, C., AND FLAHERTY, J. E. 1990. Towards the automatic numerical soluti on of partial differential equations. In Intelligent Mathematical Software Systems, E. N. Houstis, J. R. Rice, and R. Vichnevetsky, Eds. North-Holland, Amsterdam, 15-22.Google ScholarGoogle Scholar
  20. PEAaL, J. 1988. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo, Calif. Google ScholarGoogle Scholar
  21. RICE, J.R. 1976. The algorithm selection problem. Adv. Comput. 15, 65-118.Google ScholarGoogle Scholar
  22. RICE, J.R. 1979. Methodology for the algorithm selection problem. In Performance Evaluation of Numerical Software, L. D. Fosdick, Ed. North-Holland, Amsterdam, 301-307.Google ScholarGoogle Scholar
  23. RICE, J. R. AND BOISVERT, R.F. 1985. Solving Elliptic Problems Using ELLPACK. Springer- Verlag, Berlin. Google ScholarGoogle Scholar
  24. RICE, J. R., HOUSTIS, E. N., AND DYKSEN, W.R. 1981. A population of linear, second order, elliptic partial differential equations on rectangular domains, part I. Math. Comput. 36, 475-484.Google ScholarGoogle Scholar
  25. RUMELHART, U. E. AND MCCLELLAND, J. L. 1986. Parallel Distributed Processing, Explorations into the Microstructure of Cognition. MIT Press, Cambridge, Mass. Google ScholarGoogle Scholar
  26. SIu, K. Y., ROYCHOWDHURY, V., AND KALATH, T. 1995. Discrete Neural Computation. Prentice-Hall, Englewood Cliffs, N.J. Google ScholarGoogle Scholar
  27. WEERAWARANA, S. 1994. Problem solving environments for partial differential equation based applications. Ph.D. thesis, Dept. of Computer Sciences, Purdue Univ., West Lafayette, Ind. Google ScholarGoogle Scholar
  28. WEERAWARANA, S., HOUSTIS, E. N., RICE, J. R., CATLIN, A. C., CRABILL, C. L., CHUI, C. C., AND MARKUS, S. 1994. PDELab: An object-oriented framework for building problem solving environments for PDE based applications. In Proceedings of the 2nd Annual Object-Oriented Numerics Conference. Rogue-Wave Software, Corvallis, Oreg., 79-92.Google ScholarGoogle Scholar
  29. WIDROW, B. AND WINTER, R. 1988. Neural nets for adaptive filtering and adaptive pattern recognition. Computer 21, 25-39. Google ScholarGoogle Scholar
  30. ZELL, A., MACHE, N., HUB~mR, R., MAMIER, G., VOGT, M., HERRMANN, K.-U., SCHMALZL, M., SOMMER, T., HATZIGEORGIOU, A., DORING, S., AND POSSELT, D. 1993. Stuttgart Neural Network Simulator User Manual. Ver. 3.1. Tech. Rep. 3, Univ. of Stuttgart, Stuttgart, Germany.Google ScholarGoogle Scholar

Index Terms

  1. PYTHIA: a knowledge-based system to select scientific algorithms

      Recommendations

      Reviews

      Luigi Gatteschi

      This well-written paper deals with problem-solving environments, that is, with the computer systems that provide all of the computational facilities necessary to solve a target class of problems. The authors address the algorithm section problem for applications involving partial differential equations. Readers interested in the implementation and evaluation of these systems will appreciate the paper.

      Access critical reviews of Computing literature here

      Become a reviewer for Computing Reviews.

      Comments

      Login options

      Check if you have access through your login credentials or your institution to get full access on this article.

      Sign in

      Full Access

      PDF Format

      View or Download as a PDF file.

      PDF

      eReader

      View online with eReader.

      eReader