Abstract
An engineer’s model of a physical system balances accuracy and parsimony: it is as simple as possible while still accounting for the dynamical behavior of the target system. PRET is a computer program that automatically builds such models. Its inputs are a set of observations of some subset of the outputs of a nonlinear system, and its output is an ordinary differential equation that models the internal dynamics of that system. Modeling problems like this have immense and complicated search spaces, and searching them is an imposing technical challenge. PRET exploits a spectrum of AI and engineering techniques to navigate efficiently through these spaces, using a special first-order logic system to decide which technique to use when and how to interpret the results. Its representations and reasoning tactics are designed both to support this flexibility and to leverage any domain knowledge that is available from the practicing engineers who are its target audience. This flexibility and power has let PRET construct accurate, minimal models of a wide variety of applications, ranging from textbook examples to real-world engineering problems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abelson, H., Eisenberg, M., Halfant, M., Katzenelson, J., Sussman, G.J., and Yip, K., 1989, Intelligence in scientific computing, Comm. ACM.
Abelson, H. and Sussman, G.J., 1989, The Dynamicist’s Workbench I: Automatic preparation of numerical experiments, in: Symbolic Computation: Applications to Scientific Computing, R. Grossman, ed., volume 5 of Frontiers in Appl. Math. SIAM, Philadelphia.
Addanki, S., Cremonini, R., and Penberthy, J.S., 1991, Graphs of models, Artificial Intelligence 51:145–177.
Amsterdam, J., 1993, Automated qualitative modeling of dynamic physical systems, Technical Report AI-TR-1412, MIT.
Beckstein, C., Stolle, R., and Tobermann, G., 1996, Meta-programming for generalized Horn clause logic, in: META-96, Bonn, Germany, pp. 27–42.
Bradley, E. and Easley, M., 1998, Reasoning about sensor data for automated system identification, Intell. Data Analysis 2(2): 123–138.
Bradley, E., Easley, M., and Stolle, R., 2001, Reasoning about nonlinear system identification, Artificial Intelligence, in press.
Bradley, E., O’Gallagher, A., and Rogers, J., 1998, Global solutions for nonlinear systems using qualitative reasoning, Annals Math. Artif. Intell. 23:211–228.
Bradley, E. and Stolle, R., 1996, Automatic construction of accurate models of physical systems, Annals Math. Artif. Intell. 17:1–28.
Capelo, A., Ironi, L., and Tentoni, S., 1998, Automated mathematical modeling from experimental data: An application to material science, IEEE Trans. Systems, Man and Cybernetics — C 28:356–370.
Džeroski, S. and Todorovski., L., 1995, Discovering dynamics: Prom inductive logic programming to machine discovery, J. Intell. Inf. Systems 4:89–108.
Easley, M., 2000, Automating Input-Output Modeling of Dynamic Physical Systems, PhD thesis, University of Colorado at Boulder.
Easley, M. and Bradley, E., 1999, Generalized physical networks for automated model building, in: IJCAI-99, Stockholm.
Easley, M. and Bradley, E., 1999, Reasoning about input-output modeling of dynamical systems, in: IDA-99, volume 1642 of LNCS, Springer, Amsterdam, pp. 343–355.
Falkenhainer, B. and Forbus, K.D., 1991, Compositional modeling: Finding the right model for the job, Artificial Intelligence 51:95–143.
Forbus, K.D., 1984, Qualitative process theory, Artificial Intelligence 24:85–168.
Forbus, K.D., 1996, Qualitative reasoning, in: CRC Computer Science and Engineering Handbook, A.B. Tucker, Jr., ed., chapter 32, CRC Press, Boca Raton, FL, pp. 715–733.
Forrester, J., 1971, World Dynamics, Wright Allen Press, New York.
Hogan, A., Stolle, R., and Bradley, E., 1998, Putting declarative meta control to work, Technical Report CU-CS-856-98, University of Colorado at Boulder.
Huang, K.-M. and Żytkow, J.M., 1997, Discovering empirical equations from robotcollected data, in: Foundations of Intelligent Systems (ISMIS-97), Z. Ras and A. Skowron, eds., volume 1325 of LNCS, Berlin, Springer, pp. 287–297.
Kuipers, B.J., 1986, Qualitative simulation, Artificial Intelligence 29(3):289–338.
Kuipers, B.J., 1993, Reasoning with qualitative models, Artificial Intelligence 59:125–132.
Langley, P., 2000, The computational support of scientific discovery, Intl. J. Human-Computer Studies 53:393–410.
Langley, P., Simon, H.A., Bradshaw, G.L., and Żytkow, J.M., eds., 1987, Scientific Discovery: Computational Explorations of the Creative Processes, MIT Press, Cambridge, MA.
LeFèvre, J., 1997, Reactive system dynamics: An extension of Forrester’s system dynamics using bond graph-like notations, in: Bond Graph Modeling and Simulations (ICBGM-97), Phoenix, AZ, pp. 149–155.
Ljung, L., ed., 1987, System Identification; Theory for the User, Prentice-Hall, Engle-wood Cliffs, N.J.
McCarty, L.T., 1988, Clausal intuitionistic logic I. Fixed-point semantics, J. Logic Programming 5:1–31.
Morrison, F., 1991, The Art of Modeling Dynamic Systems, Wiley, New York.
Mosterman, P.J. and Biswas, G., 1997, Formal specifications for hybrid dynamical systems, in: IJCAI-97, Nagoya, Japan, pp. 568–573.
Nayak, P.P., 1995, Automated Modeling of Physical Systems, volume 1003 of LNCS, Springer, Berlin.
Paynter, H., 1961, Analysis and Design of Engineering Systems, MIT Press, Cambridge, MA.
Stolle, R., 1998, Integrated Multimodal Reasoning for Modeling of Physical Systems, PhD thesis, University of Colorado, to appear in LNCS, Springer, Heidelberg.
Stolle, R. and Bradley, E., 1998, Multimodal reasoning for automatic model construction, in: AAAI-98, Madison, Wisconsin, pp. 181–188.
Sussman, G.J. and Steele, G.L., 1980, CONSTRAINTS — a language for expressing almost hierarchical descriptions, Artificial Intelligence 14:1–39.
Todorovski, L. and Džeroski, S., 1997, Declarative bias in equation discovery, in: ICML-97, Morgan Kaufmann, San Francisco, pp. 376–384.
Top, J. and Akkermans, H., 1991, Computational and physical causality, in: IJCAI-91.
Washio, T., Motoda, H., and Yuji, N., 1999, Discovering admissible model equations from observed data based on scale-types and identity constraints, in: IJCAI-99, pp. 772–779.
Weld, D.S. and de Kleer, J., eds., 1990, Readings in Qualitative Reasoning About Physical Systems, Morgan Kaufmann, San Mateo CA.
Żytkow, J.M., 1999, Model construction: elements of a computational mechanism, in: Conference on Creativity, Edinburgh, April.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Stolle, R., Easley, M., Bradley, E. (2002). Reasoning about Models of Nonlinear Systems. In: Magnani, L., Nersessian, N.J., Pizzi, C. (eds) Logical and Computational Aspects of Model-Based Reasoning. Applied Logic Series, vol 25. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0550-0_12
Download citation
DOI: https://doi.org/10.1007/978-94-010-0550-0_12
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-0791-0
Online ISBN: 978-94-010-0550-0
eBook Packages: Springer Book Archive