A Machine Learning and Equation Signature Approach to Equation Discovery

Systematic Methods of Scientific Discovery

Volume

Systematic Methods of Scientific Discovery

Contents

This paper introduces a novel method for equation discovery, called equation signatures. This algorithm casts equation discovery as a search for transformations which reshape the data into identifiable equation type, independent of the equation’s coefficients. This technique enables discovery of equations for the N-dimensional case where there are no subsets of constant variables in the dataset. The set of transforms that this procedure considers at present includes the power transforms, powers of logarithms, and exponentials of power transforms. The software selects the final equation from a group of 'best' equations based on attributes. Results are presented for blackbody radiation data and part of Cullen Schaffer’s 'function-finding.data' dataset.