On the Context of Dimensional Analysis in Artificial Intelligence

Dimensional Analysis is a well-established modeling technique which employs domain knowledge in form of the physical dimensions of the model parameters. Based on the principle of dimensional homogeneity, the physical dimension information about the model parameters is used to reduce the combinatorial complexity in the search for the correct model. Due to the philosophical foundation of the homogeneity principle, which is an universal modeling thought construct, this universal principle holds in any modeling area, where model parameters with physical dimensions occur. The transfer of similarity methods from engineering to artificial intelligence is possible because both domains share common objects such as real-valued sensor data. The use of group transforms as formally guaranteed by the Pi-Theorem of Buckingham is therefore straightforward in the modeling of many real-valued artificial intelligence techniques. The strength of the method of dimensional analysis in different areas of artificial intelligence such as in case-based reasoning, pattern recognition, genetic algorithms, design evaluation, neural networks and others, is shown using the example of the topology and generalization properties in non-linear neural networks. The results provide some insight into the modeling power of dimensional analysis in artificial intelligence techniques.