# Active Learning in Symbolic Regression with Physical Constraints

arXiv: https://arxiv.org/abs/2305.10379 · HTML: https://mlsanity.com/paper/2305.10379/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 42 references that are in the map.
- First posted on arXiv 17 May 2023.

## Builds on (most cited first, 7 of 7)

- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [A Bayesian machine scientist to aid in the solution of challenging scientific problems](https://mlsanity.com/paper/2004.12157/) (2020)
- [Deep symbolic regression for physics guided by units constraints: toward the automated discovery of physical laws](https://mlsanity.com/paper/2303.03192/) (2023)
- [Symbolic Pregression: Discovering Physical Laws from Distorted Video](https://mlsanity.com/paper/2005.11212/) (2020)
- [Fundamental limits to learning closed-form mathematical models from data](https://mlsanity.com/paper/2204.02704/) (2022)
- [Active Learning Improves Performance on Symbolic RegressionTasks in StackGP](https://mlsanity.com/paper/2202.04708/) (2022)
- [Incorporating Background Knowledge in Symbolic Regression using a Computer Algebra System](https://mlsanity.com/paper/2301.11919/) (2023)

## Built on by (most cited first, 3 of 3)

- [In Context Learning and Reasoning for Symbolic Regression with Large Language Models](https://mlsanity.com/paper/2410.17448/) (2024)
- [Active Symbolic Discovery of Ordinary Differential Equations via Phase Portrait Sketching](https://mlsanity.com/paper/2409.01416/) (2024)
- [Discovering an interpretable mathematical expression for a full wind-turbine wake with artificial intelligence enhanced symbolic regression](https://mlsanity.com/paper/2406.00695/) (2024)

## Abstract (arXiv)

Evolutionary symbolic regression (SR) fits a symbolic equation to data, which gives a concise interpretable model. We explore using SR as a method to propose which data to gather in an active learning setting with physical constraints. SR with active learning proposes which experiments to do next. Active learning is done with query by committee, where the Pareto frontier of equations is the committee. The physical constraints improve proposed equations in very low data settings. These approaches reduce the data required for SR and achieves state of the art results in data required to rediscover known equations.