Extrapolation and learning equations
This addresses the need for interpretable models in fields like natural sciences, offering a novel approach to function learning.
The paper tackles the problem of learning interpretable analytical expressions from data, proposing an equation learner network that can extrapolate to unseen domains and often identifies the true underlying source expression.
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.