Discovery of first-principle equations based on scale-type-based and data-driven reasoning

Abstract

We propose a novel approach to automatically discover formulae of first principles from measurement data. The formulae obtained by our approach are ensured to reflect first principles despite the fact that we try to use as little knowledge of the target relation as possible to make it applicable to various domains not limited to physics problems. The basic idea is the combined use of deductive ‘scale-type-based reasoning’ and ‘data-driven reasoning’. The former is based on scale-type information on quantities different from the quantity dimension. The features of our approach are demonstrated and discussed through its application to many classes of examples. This approach is expected to provide a basis for discovering the first principles of various domains such as physics, biology, psychology, economics and social science.