Discovering Admissible Model Equations from Observed Data Based on Scale-Types and Identity Constrains

Most conventional law equation discovery systems such as BACON require experimental environments to acquire their necessary data. The mathematical techniques such as linear system identi cation and neural network tting presume the classes of equations to model given observed data sets. The study reported in this paper proposes a novel method to discover an admissible model equation from a given set of observed data, while the equation is ensured to re ect rst principles governing the objective system. The power of the proposed method comes from the use of the scale-types of the observed quantities, a mathematical property of identity and quasi-bi-variate tting to the given data set. Its principles and algorithm are described with moderately complex examples, and its practicality is demonstrated through a real application to psychological and sociological law equation discovery.