  In classical machine learning, regression is treated as a black box process
of identifying a suitable function from a hypothesis set without attempting to
gain insight into the mechanism connecting inputs and outputs. In the natural
sciences, however, finding an interpretable function for a phenomenon is the
prime goal as it allows to understand and generalize results. This paper
proposes a novel type of function learning network, called equation learner
(EQL), that can learn analytical expressions and is able to extrapolate to
unseen domains. It is implemented as an end-to-end differentiable feed-forward
network and allows for efficient gradient based training. Due to sparsity
regularization concise interpretable expressions can be obtained. Often the
true underlying source expression is identified.
