Equation discovery  Introduction
introduction 
Lagrange and Lagramge 
towards knowledgebased equation discovery
What is the task of equation discovery?
Equation discovery is the area of machine learning that develops methods for
automated discovery of quantitative laws, expressed in the form of equations,
in collections of measured data. It is strongly related to the area of system
identification. However, mainstream system identification methods work under
the assumption that the structure of the model, i.e., the form of the
equations, is known and are concerned with determining the values of the
constant parameters in the model that minimize the discrepancy between
measured and simulated data. Equation discovery systems, on the other hand,
aim at identifying both an adequate structure of the equations and appropriate
values of the constant parameters. Again, the discrepancy between measured and
simulated data is to be minimized.
A very brief overview of the equation discovery systems

BACON
[Langley et al. 1987]
is the pioneer among equation discovery systems. It uses a set of datadriven
heuristics for finding regularities (constancies and trends) in data and for
formulating hypotheses based on them.

COPER
[Kokar 1986] is using information about the dimension
units of the system variables to restrict the space of possible equation
structures.

FAHRENHEIT/EF
[Langley and Zytkow 1989],
[Zembowitz and Zytkow 1992]
 EF (Equation Finder) is used as a equation discovery
subsystem of the scientific discovery system FAHRENHEIT.
Used for discovering bivariate equations only, user being able to specify the
set of operators and functions to be used within equations.

ABACUS
[Falkenhainer and Michalski 1990]
is experimenting with different search strategies through the space of
equation structures. Also allows discovery of piecewise equations using
clustering for identifying the limits between pieces.

IDS
[Nordhausen and Langley 1990]

ARC
[Moulet 1992]

E*
[Schaffer 1993] discovery of bivariate equations
using a small set of predefined equation structures.

LAGRANGE
[Dzeroski and Todorovski 1995] extends
the scope of the equation discovery systems towards the discovery of
differential equations.

GOLDHORN
[Krizman et al. 1995] extends
LAGRANGE towards discovery from noisy data.

SDS
[Washio and Motoda 1997] using information
about scale types of the dimension units of the system variables to restrict
the space of possible equations.

LAGRAMGE
[Todorovski and Dzeroski 1997] allows
the user to specify the space of possible equations with context free grammar.
Bibliography

Dzeroski, S. and Todorovski, L. (1995)
Discovering dynamics: From inductive logic programming to machine discovery.
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Falkenhainer, B. and Michalski, R. (1990)
Integrating quantitative and qualitative discovery in the ABACUS system.
In Kodratoff, Y. and Michalski, R. (editors) Machine Learning: An Artificial Intelligence Approach.
Morgan Kaufmann, San Mateo, CA.

Kokar, M.M. (1986)
Determining arguments of invariant functional descriptions.
Machine Learning, 1(4): 403422.

Krizman, V., Dzeroski, S. and Kompare, B. (1995)
Discovering dynamics from measured data.
Electrotechnical Review, 62: 191198.

Langley, P., Simon, H. and Bradshaw, G. (1987)
Heuristics for empirical discovery.
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Springer, Berlin.

Langley, P. and Zytkow, J. (1989)
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Moulet, M. (1992)
Iterative Model Construction with Regression.

Nordhausen, B. and Langley, P. (1990)
A Robust Approach to Numeric Discovery.
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Schaffer, C. (1993)
Bivariate scientific function finding in a sampled, realdata testbed.
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Todorovski, L. and Dzeroski, S. (1997)
Declarative bias in equation discovery.
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Washio, T. and Motoda, H. (1997)
Discovering admissible models of complex systems based on scaletypes and identity constraints.
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Zembowitz, R. and Zytkow, J. (1992)
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