Comparing three error criteria for selecting radial basis function network topology

• Published in: Computer methods in applied mechanics and engineering 2009-05, Vol.198 (27), p.2137-2150
• Main Authors: Goel, Tushar, Stander, Nielen
• Format: Article
• Language: English
• Subjects: Computational techniques; Crashworthiness; Cross-validation; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Inelasticity (thermoplasticity, viscoplasticity...); Mathematical methods in physics; Metamodels; Physics; Radial basis functions network; Solid mechanics; Structural and continuum mechanics; Topology selection criterion
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2009.02.016

The performance of radial basis function networks largely depends on the choice of topology i.e., location and number of centers, radius of influence, etc. Thus finding the best network is a multi-level optimization problem. It is obvious that different criteria for optimization would result in different network topologies. A systematic study is carried out to compare the most widely used root mean square error criterion for topology selection with cross-validation based methods like PRESS or PRESS-ratio. The main focus here is to find the best criterion to select RBF network topology. Based on a suite of analytical examples and crashworthiness simulation problems, it was concluded that the PRESS-based selection criterion performs the best and offers the least variation with the choice of experimental design, sampling density, and the nature of the problem.