Similarity-Based Equational Inference in Physics

TL;DR

This paper introduces a method to convert informal handwritten physics derivations into datasets and uses symbolic similarity heuristics to automate equation reconstruction, advancing the automation of physics derivations.

Contribution

It presents a novel dataset creation method and a symbolic similarity heuristic for automating equation inference in physics derivations.

Findings

Successfully reconstructed equations using similarity-based search.

Demonstrated the approach on a condensed matter physics example.

Laid groundwork for multi-hop equational inference in physics.

Abstract

Automating the derivation of published results is a challenge, in part due to the informal use of mathematics by physicists, compared to that of mathematicians. Following demand, we describe a method for converting informal hand-written derivations into datasets, and present an example dataset crafted from a contemporary result in condensed matter. We define an equation reconstruction task completed by rederiving an unknown intermediate equation posed as a state, taken from three consecutive equational states within a derivation. Derivation automation is achieved by applying string-based CAS-reliant actions to states, which mimic mathematical operations and induce state transitions. We implement a symbolic similarity-based heuristic search to solve the equation reconstruction task as an early step towards multi-hop equational inference in physics.