AI Descartes: Combining Data and Theory for Derivable Scientific
  Discovery
  Scientists have long aimed to discover meaningful formulae which accurately
describe experimental data. One common approach is to manually create
mathematical models of natural phenomena using domain knowledge, then fit these
models to data. In contrast, machine-learning algorithms automate the
construction of accurate data-driven models while consuming large amounts of
data. Ensuring that such models are consistent with existing knowledge is an
open problem. We develop a method for combining logical reasoning with symbolic
regression, enabling principled derivations of models of natural phenomena. We
demonstrate these concepts for Kepler's third law of planetary motion,
Einstein's relativistic time-dilation law, and Langmuir's theory of adsorption,
automatically connecting experimental data with background theory in each case.
We show that laws can be discovered from few data points when using formal
logical reasoning to distinguish the correct formula from a set of plausible
formulas that have similar error on the data. The combination of reasoning with
machine learning provides generalizable insights into key aspects of natural
phenomena. We envision that this combination will enable derivable discovery of
fundamental laws of science. We believe that this is a crucial first step for
connecting the missing links in automating the scientific method.
