In order to design a numerical model of a physical structure, the modeller must decide the appropriate resolution for modelling each component part, a task requiring considerable expertise. Too fine a mesh will cause unnecessary computational overheads when running the model, whereas too coarse a mesh will produce intolerable approximation errors.
We have used ILP to induce, from examples provided by expert modellers, rules for choosing appropriate resolution values. One advantage of ILP is that the examples and rules are expressed in predicate logic, so predicates can be used to describe geometric relations between different elements. Without such expressiveness, it would be impossible to adequately describe the structure being modelled.
The data here is from experiments conducted with Golem as reported in [Dolsak B. and Muggleton S. (1992)].
The task is to learn rules for the number of elements using the following information:
Edgeis an edge label (unique for each edge) and
Number_of_elementsis the number of elements on the edge denoted by label
Edge. The number of elements on an edge varies from 1 to 17.
opposite/2, as well as the relation
Dolsak B. and Muggleton S. (1992).
The application of Inductive Logic Programming to finite element mesh design.
In S. Muggleton editor, Inductive Logic Programming, Academic Press, London.