Automated discovery of empirical equations from data

Abstract

We describe a machine discovery system for automated finding regularities in numerical data. It can detect a broad range of empirical equations useful in different sciences, and can be easily expanded by addition of new variable transformations. Our system treats experimental error and evaluation of equations in a systematic and statistically sound manner in contradistinction to systems such as BACON, ABACUS, which include error-related parameters, but disregard problems of error analysis and propagation, leading to paradoxical results. Our system propagates error to the transformed variables and assigns error to parameters in equations. Furthermore, it uses errors in weighted least squares fitting, in the evaluation of equations, including their acceptance, rejection and ranking, and uses parameter error to eliminate spurious parameters. In the last part of our paper we analyse the evaluation of equation finding systems. We introduce two convergence tests and we analyze the performance of our system on those tests.