# Similarity-Based Equational Inference in Physics

arXiv: https://arxiv.org/abs/2103.13496 · HTML: https://mlsanity.com/paper/2103.13496/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 31 references that are in the map.
- First posted on arXiv 24 Mar 2021.

## Builds on (most cited first, 13 of 13)

- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1708.00588/) (2017)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [Discovering physical concepts with neural networks](https://mlsanity.com/paper/1807.10300/) (2018)
- [Integration of Neural Network-Based Symbolic Regression in Deep Learning for Scientific Discovery](https://mlsanity.com/paper/1912.04825/) (2019)
- [Compositional Questions Do Not Necessitate Multi-hop Reasoning](https://mlsanity.com/paper/1906.02900/) (2019)
- [Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks](https://mlsanity.com/paper/1905.04817/) (2019)
- [Reinforcement Learning of Theorem Proving](https://mlsanity.com/paper/1805.07563/) (2018)
- [Symbolic Pregression: Discovering Physical Laws from Distorted Video](https://mlsanity.com/paper/2005.11212/) (2020)
- [A General Deep Learning Framework for Network Reconstruction and Dynamics Learning](https://mlsanity.com/paper/1812.11482/) (2018)
- [Toward an AI Physicist for Unsupervised Learning](https://mlsanity.com/paper/1810.10525/) (2018)
- [Learning Equational Theorem Proving](https://mlsanity.com/paper/2102.05547/) (2021)
- [Automatic Derivation Of Formulas Using Reforcement Learning](https://mlsanity.com/paper/1808.04946/) (2018)

## Built on by (most cited first, 4 of 4)

- [A Survey in Mathematical Language Processing](https://mlsanity.com/paper/2205.15231/) (2022)
- [FormalScience: Scalable Human-in-the-Loop Autoformalisation of Science with Agentic Code Generation in Lean](https://mlsanity.com/paper/2604.23002/) (2026)
- [PhysNLU: A Language Resource for Evaluating Natural Language Understanding and Explanation Coherence in Physics](https://mlsanity.com/paper/2201.04275/) (2022)
- [Exploring the Limits of Fine-grained LLM-based Physics Inference via Premise Removal Interventions](https://mlsanity.com/paper/2404.18384/) (2024)

## Abstract (arXiv)

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.