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:
mesh(Edge,Number_of_elements)
, where Edge
is an edge label
(unique for each edge) and Number_of_elements
is the number
of elements on the edge denoted by label Edge
. The number of elements
on an edge varies from 1 to 17.
important_long
, important
,
important_short
, not_important
, circuit
,
half_circuit
, quarter_circuit
, short_for_hole
,
long_for_hole
, circuit_hole
, half_circuit_hole
and
quarter_circuit_hole
.
free
,
one_side_fixed
, two_side_fixed
or fixed
.
not_loaded
,
one_side_loaded
, two_side_loaded
or
continuously_loaded
.
neighbour/2
and opposite/2
, as well as the
relation equal/2
.
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.