On Modeling Assumptions and Artificial Neural Networks

As a consequence of the epistemological principle of dimensional homogeneity follows the existence proof for the so-called Pi-Theorem, which is valid for all dimensionally homogeneous function equations. Any real-valued functional model from biology, chemistry, physics and engineering can therefore be subjected to a so-called similarity transform and be checked with the Pi-Theorem. This is possible because it is generally agreed on that any dimensionally not homogeneous model cannot be correct. As an interdisciplinary example, the construction of artificial neural networks (ANN) models currently used in many applications for function approximation based on a set of input-output patterns is subjected to this principle of dimensional homogeneity. Several important restrictions, properties and conclusions about the ANN generalization are then proved by the Pi-Theorem and justified by the principle of dimensional homogeneity.