Equation discovery systems - Lagrange and Lagramge

LAGRANGE

LAGRANGE is an equation discovery system capable of discovering differential as well as ordinary algebraic equations involving more than two variables from observational data only. This is in contrast with early equation discovery systems, which perform problem decomposition to discover equations involving more than two variables. These systems keep all but two variables constant and require experiments that vary the remaining two. However, this is impossible in many cases, especially in the context of dynamic systems, as the scientist might not have full experimental control over each system variable. For additional information consult [Dzeroski and Todorovski, 1993], [Dzeroski and Todorovski, 1995].

LAGRANGE is implemented in the C programming language using the Gnu gcc compiler. It was developed on a Sun workstation working under the SunOS operation system. It was successfully compiled and run on Hewlett Packard (HP-UX 10.01), Sun (SunOS 4.1.3) and PC (under the Windows 95/NT and Linux operating systems, compiled using the gcc compiler) workstations.

Download LAGRANGE source code (tested on various platforms using gcc)
Download LAGRANGE user's manual (postscript)

LAGRAMGE

The equation discovery system LAGRAMGE (this is a deliberate misspelling of the name of the equation discovery system LAGRANGE, the predecessor of LAGRAMGE. The letter N is replaced with M, so that the second part of the acronym reads GRAM as in grammar) incorporates methods for using theoretical knowledge from the modeled domain in the process of equation discovery. In contrast with classical system identification methods, where the structure of the model has to be explicitly provided by the human expert, LAGRAMGE can use a more sophisticated method (based on context free grammars) for specifying a whole range of possible models that make sense from the expert's point of view. For additional information consult [Todorovski and Dzeroski, 1997], [Todorovski, 1998].

LAGRAMGE is implemented in the C programming language using the Gnu gcc compiler. It was developed on a Hewlett Packard workstation working under the HP-UX operation system. It was successfully compiled and run on Hewlett Packard (HP-UX 10.20, compiled with gcc), Sun (Solaris 2.6, compiled with gcc) and PC (Linux RedHat 6.1) workstations.

Download LAGRAMGE source code (prepared for Linux RedHat 6.1)
Download LAGRAMGE source code (prepared for Solaris 2.6/gcc)
Download LAGRAMGE source code (prepared for HP-UX 10.20/gcc)
Download LAGRAMGE user's manual (postscript)

References

1. Dzeroski, S. and Todorovski, L. (1993) Discovering dynamics. In Proc. Tenth International Conference on Machine Learning, pages 97-103. Morgan Kaufmann, San Mateo, CA.
2. Dzeroski, S. and Todorovski, L. (1995) Discovering dynamics: from inductive logic programming to machine discovery. Journal of Intelligent Information Systems, 4: 89-108.
3. Todorovski, L. and Dzeroski, S. (1997) Declarative bias in equation discovery. In Proc. Fourteenth International Conference on Machine Learning, pages 376-384. Morgan Kaufmann, San Mateo, CA.
4. Todorovski, L. (1998) Declarative bias in equation discovery. M.Sc. Thesis. Faculty of Computer and Information Science, Ljubljana, Slovenia.