Informed Equation Learning

TL;DR

This paper introduces an informed equation learning system that incorporates expert knowledge and structured priors to learn interpretable, high-accuracy equations from data, especially handling atomic functions with singularities.

Contribution

It presents a novel system that integrates domain knowledge and structured sparsity priors to improve the learning of interpretable equations in scientific and engineering contexts.

Findings

Successfully learned interpretable models with high predictive accuracy.

Effectively handled atomic functions with singularities like logarithm and division.

Demonstrated applicability on artificial and real-world engineering data.

Abstract

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.