  Distilling data into compact and interpretable analytic equations is one of
the goals of science. Instead, contemporary supervised machine learning methods
mostly produce unstructured and dense maps from input to output. Particularly
in deep learning, this property is owed to the generic nature of simple
standard link functions. To learn equations rather than maps, standard
non-linearities can be replaced with structured building blocks of atomic
functions. However, without strong priors on sparsity and structure,
representational complexity and numerical conditioning limit this direct
approach. To scale to realistic settings in science and engineering, we propose
an informed equation learning system. It provides a way to incorporate expert
knowledge about what are permitted or prohibited equation components, as well
as a domain-dependent structured sparsity prior. Our system then utilizes a
robust method to learn equations with atomic functions exhibiting
singularities, as e.g. logarithm and division. We demonstrate several
artificial and real-world experiments from the engineering domain, in which our
system learns interpretable models of high predictive power.
