# Incorporating Background Knowledge in Symbolic Regression using a Computer Algebra System

arXiv: https://arxiv.org/abs/2301.11919 · HTML: https://mlsanity.com/paper/2301.11919/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 54 references that are in the map.
- First posted on arXiv 27 Jan 2023.

## Builds on (most cited first, 10 of 10)

- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Underspecification Presents Challenges for Credibility in Modern Machine Learning](https://mlsanity.com/paper/2011.03395/) (2020)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [A Bayesian machine scientist to aid in the solution of challenging scientific problems](https://mlsanity.com/paper/2004.12157/) (2020)
- [A computational framework for physics-informed symbolic regression with straightforward integration of domain knowledge](https://mlsanity.com/paper/2209.06257/) (2022)
- [Shape-constrained Symbolic Regression -- Improving Extrapolation with Prior Knowledge](https://mlsanity.com/paper/2103.15624/) (2021)
- [Interpretable and Explainable Machine Learning for Materials Science and Chemistry](https://mlsanity.com/paper/2111.01037/) (2021)
- [Fast, accurate, and transferable many-body interatomic potentials by symbolic regression](https://mlsanity.com/paper/1904.01095/) (2019)
- [AI Descartes: Combining Data and Theory for Derivable Scientific Discovery](https://mlsanity.com/paper/2109.01634/) (2021)
- [Logic Guided Genetic Algorithms](https://mlsanity.com/paper/2010.11328/) (2020)

## Built on by (most cited first, 2 of 2)

- [Active Learning in Symbolic Regression with Physical Constraints](https://mlsanity.com/paper/2305.10379/) (2023)
- [Automatic Ordinary Differential Equations Discovery For Biological Systems Using Large Language Model Powered Agentic System](https://mlsanity.com/paper/2607.13608/) (2026)

## Abstract (arXiv)

Symbolic Regression (SR) can generate interpretable, concise expressions that fit a given dataset, allowing for more human understanding of the structure than black-box approaches. The addition of background knowledge (in the form of symbolic mathematical constraints) allows for the generation of expressions that are meaningful with respect to theory while also being consistent with data. We specifically examine the addition of constraints to traditional genetic algorithm (GA) based SR (PySR) as well as a Markov-chain Monte Carlo (MCMC) based Bayesian SR architecture (Bayesian Machine Scientist), and apply these to rediscovering adsorption equations from experimental, historical datasets. We find that, while hard constraints prevent GA and MCMC SR from searching, soft constraints can lead to improved performance both in terms of search effectiveness and model meaningfulness, with computational costs increasing by about an order-of-magnitude. If the constraints do not correlate well with the dataset or expected models, they can hinder the search of expressions. We find Bayesian SR is better these constraints (as the Bayesian prior) than by modifying the fitness function in the GA