Enhancing the plausibility of law equation discovery through cross check among multiple scale-type-based models

The study in the field of scientific discovery from data has been directed to the discovery of plausible law equations representing the first principles underlying objective systems. In this paper, a novel principle and an algorithm to predictively discover new scientific law equation formulae consisting of newly given quantities are proposed based on the candidate law equations governing the other quantities under current observation. The first principle-based scientific law equation formulae must follow some mathematical admissibility and consistency. These conditions enable efficient reasoning of the law equation formulae in the prediction process. The soundness and the reproducibility of the equation prediction by this approach have been tested through numerical simulations of physical examples, and, moreover, its practicality has been confirmed through a real socio-psychological analysis. The approach can discover a set of scientific law equations representing common first principles under different set of quantities, and enables to capture general scietific features of the objective system under analysis.