  We develop a symbolic regression framework for extracting the governing
mathematical expressions from observed data. The evolutionary approach, faiGP,
is designed to leverage the properties of a function algebra that have been
encoded into a grammar, providing a theoretical guarantee of universal
approximation and a way to minimize bloat. In this framework, the choice of
operators of the grammar may be informed by a physical theory or symmetry
considerations. Since there is currently no theory that can derive the
'constants of nature', an empirical investigation on extracting these
coefficients from an evolutionary process is of methodological interest. We
quantify the impact of different types of regularizers, including a diversity
metric adapted from studies of the transcriptome and a complexity measure, on
the performance of the framework. Our implementation, which leverages neural
networks and a genetic programmer, generates non-trivial symbolically
equivalent expressions ("Ramanujan expressions") or approximations with
potentially interesting numerical applications. To illustrate the framework, a
model of ligand-receptor binding kinetics, including an account of gene
regulation by transcription factors, and a model of the regulatory range of the
cistrome from omics data are presented. This study has important implications
on the development of data-driven methodologies for the discovery of governing
equations in experimental data derived from new sensing systems and
high-throughput screening technologies.
