Model simplification by asymptotic order of magnitude reasoning

Artificial Intelligence

Volumn 80, Issue 2, 1996, Pages 309-348

  Yip, Kenneth Man kam ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTER SOFTWARE; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS;

ASYMPTOTIC ORDER OF MAGNITUDE REASONING; MODEL SIMPLIFICATION; NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS;

LEARNING SYSTEMS;

EID: 0030086035     PISSN: 00043702     EISSN: None     Source Type: Journal    
DOI: 10.1016/0004-3702(94)00068-9     Document Type: Article

References (33)

1. H. Abelson, M. Eisenberg, M. Halfant, M. Katzenelson, E. Sacks, G. Sussman, J. Wisdom and K. Yip, Intelligence in scientific computing, Commun. ACM 32 (5) (1989).
2. C. Bender and S. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978).
3. S.W. Bennett, Approximation in mathematical domains, in: Proceedings AAAI-87, Seattle, WA (1987).
4. W.W. Bledsoe, A new method for proving certain presburger formulas, in: Proceedings IJCAI-75, Tblisi, Georgia (1975).
5. E. Bradley and F. Zhao, Phase space control system design, IEEE Control Syst. Mag. 13 (1993).
6. R.A. Brooks, Symbolic reasoning among 3-D models and 2-D images, Artif. Intell. 17 (1981) 285-348.
7. A. Bundy, The Computer Modelling of Mathematical Reasoning (Academic Press, New York, 1983).
8. T.H. Cormen, C. Leiserson and R. Rivest, Introduction to Algorithms (McGraw-Hill, New York, 1989).
9. J. de Kleer and B.C. Williams, eds., Qualitative Reasoning about Physical Systems II (Special Volume) Artif. Intell. 51 (1991).
10. A. Erdelyi, Asymptotic Expansions (Dover, New York, 1956).
11. G.H. Hardy, Orders of Infinity, Cambridge Tracts 12 (Cambridge University Press, Cambridge, 2nd ed., 1924).
12. J. Kevorkian and J.D. Cole, Perturbation Methods in Applied Mathematics (Springer-Verlag, New York, 1981).
13. C.C. Lin and L.A. Segel, Mathematics Applied to Deterministic Problems in the Natural Sciences (MacMillan, New York, 1974).
14. M.L. Mavrovouniotis and G. Stephanopoulos, Formal order-of-magnitude reasoning in process engineering, Comput. Chem. Eng. 12 (1988).
15. C.C. Mei, The Applied Dynamics of Ocean Surface Waves (World Scientific, 1989).
16. J. Moran, An Introduction to Theoretical and Computational Aerodynamics (Wiley, New York, 1984).
17. S. Murthy, Qualitative reasoning at multiple resolutions, in: Proceedings AAAI-88, St. Paul, MN (1988).
18. P.P. Nayak, Order of magnitude reasoning using logarithms, in: Proceedings 7th International Workshop on Qualitative Reasoning, San Juan Island, WA (1993).
19. O. Raiman, Order of magnitude reasoning, in: Proceedings AAAI-86, Philadelphia, PA (1986).
20. O. Raiman, Order of magnitude reasoning, Artif. Intell. 51 (1991) 11-38.
21. E.P. Sacks, Hierarchical reasoning about inequalities, in: Proceedings AAAI-87, Seattle, WA (1987).
22. R.E. Shostak, On the SUP-INF method for proving Presburger formulas, J. ACM 24 (1977).
23. R. Simmons, Commonsense arithmetic reasoning, in: Proceedings AAAI-86, Philadelphia. PA (1986).
24. K. Stewartson, Multistructured boundary layers on flat plates and relations bodies, Adv. Appl. Mech. 14 (1974).
25. J.L. Tennekes and H. Lumley, A First Course in Turbulence (MIT Press, Cambridge, MA, 1972).
26. M. Van Dyke, Perturbation Methods in Fluid Mechanics (The Parabolic Press, annotated edition, 1975).
27. D.S. Weld, Exaggeration, Artif. Intell. 43 (1990) 311-368.
28. B.C. Williams and O. Raiman, Caricatures: generating models of dominant behaviors, in: Proceedings 6th International Workshop on Qualitative Reasoning (1992).
29. K.G. Wilson, Problems in physics with many scales of length, Sci. American 241 (1979).
30. C. Yih, Fluid Mechanics (West River Press, 1977).
31. K. Yip, Computer aided heuristic and qualitative reasoning in fluid mechanics, in: E.N. Houstis and J.R. Rice, eds., Artificial Intelligence, Expert Systems, and Symbolic Computing (Elsevier Science Publishers, Amsterdam, 1992).
32. K. Yip, Model simplifications in fluid mechanics, in: Proceedings AAAI-93, Washington, DC (1993).
33. F. Zhao, Extracting and representing qualitative behaviors of complex systems in phase spaces, in: Proceedings IJCAI-91, Sydney, Australia (1991).