Knowledge base for finite-element mesh design learned by inductive logic programming

Abstract

This paper addresses an important application of machine learning (ML) in design. One of the major bottlenecks in the process of engineering analysis by using the finite-element method—a design of the finite-element mesh—was a subject of improvement. Defining an appropriate geometric mesh model that ensures low approximation errors and avoids unnecessary computational overhead is a very difficult and time-consuming task based mainly on the user's experience. A knowledge base for finite-element mesh design has been constructed using the ML techniques. Ten mesh models have been used as a source of training examples. The mesh dataset was probably the first real-world relational dataset and became one of the most widely used training set for experimenting with inductive logic programming (ILP) systems. After several experiments with different ML systems in the last few years, the ILP system CLAUDIEN was chosen to construct the rules for determining the appropriate mesh resolution values. The ILP has been found to be an effective approach to the problem of mesh design. An evaluation of the resulting knowledge base shows that the mesh design patterns are captured well by the induced rules and represent a solid basis for practical application. The aim of this paper is not only to present the real-life ML application to design, but also to describe and discuss a relation of the work being done to the topic of this special issue: the proposed “dimensions” of ML in design.