Integration of Data and Theory for Accelerated Derivable Symbolic Discovery

Scientists have long aimed to discover meaningful equations which accurately describe data. Machine learning algorithms automate construction of accurate data-driven models, but ensuring that these are consistent with existing knowledge is a challenge. We developed a methodology combining automated theorem proving with symbolic regression, enabling principled derivations of laws of nature. We demonstrate this for Kepler's third law, Einstein's relativistic time dilation, and Langmuir's theory of adsorption, in each case, automatically connecting experimental data with background theory. The combination of logical reasoning with machine learning provides generalizable insights into key aspects of the natural phenomena.