Our physics-inspired algorithm for symbolic regression is able to discover complex physics equations from mere tables of numbers. A core challenge for both physics and artificial intelligence (AI) is symbolic regression: finding a symbolic expression that matches data from an unknown function. Although this problem is likely to be NP-hard in principle, functions of practical interest often exhibit symmetries, separability, compositionality, and other simplifying properties. In this spirit, we develop a recursive multidimensional symbolic regression algorithm that combines neural network fitting with a suite of physics-inspired techniques. We apply it to 100 equations from the Feynman Lectures on Physics, and it discovers all of them, while previous publicly available software cracks only 71; for a more difficult physics-based test set, we improve the state-of-the-art success rate from 15 to 90\%.
%0 Journal Article
%1 doi:10.1126/sciadv.aay2631
%A Udrescu, Silviu-Marian
%A Tegmark, Max
%D 2020
%J Science Advances
%K ak-symbolic-numeric app_physics
%N 16
%P eaay2631
%R 10.1126/sciadv.aay2631
%T AI Feynman: A physics-inspired method for symbolic regression
%U https://www.science.org/doi/abs/10.1126/sciadv.aay2631
%V 6
%X Our physics-inspired algorithm for symbolic regression is able to discover complex physics equations from mere tables of numbers. A core challenge for both physics and artificial intelligence (AI) is symbolic regression: finding a symbolic expression that matches data from an unknown function. Although this problem is likely to be NP-hard in principle, functions of practical interest often exhibit symmetries, separability, compositionality, and other simplifying properties. In this spirit, we develop a recursive multidimensional symbolic regression algorithm that combines neural network fitting with a suite of physics-inspired techniques. We apply it to 100 equations from the Feynman Lectures on Physics, and it discovers all of them, while previous publicly available software cracks only 71; for a more difficult physics-based test set, we improve the state-of-the-art success rate from 15 to 90\%.
@article{doi:10.1126/sciadv.aay2631,
abstract = {Our physics-inspired algorithm for symbolic regression is able to discover complex physics equations from mere tables of numbers. A core challenge for both physics and artificial intelligence (AI) is symbolic regression: finding a symbolic expression that matches data from an unknown function. Although this problem is likely to be NP-hard in principle, functions of practical interest often exhibit symmetries, separability, compositionality, and other simplifying properties. In this spirit, we develop a recursive multidimensional symbolic regression algorithm that combines neural network fitting with a suite of physics-inspired techniques. We apply it to 100 equations from the Feynman Lectures on Physics, and it discovers all of them, while previous publicly available software cracks only 71; for a more difficult physics-based test set, we improve the state-of-the-art success rate from 15 to 90\%.},
added-at = {2024-01-22T09:30:03.000+0100},
author = {Udrescu, Silviu-Marian and Tegmark, Max},
biburl = {https://www.bibsonomy.org/bibtex/2a8e96edede4cb84ab0e8bcc011585bd9/martinr},
doi = {10.1126/sciadv.aay2631},
eprint = {https://www.science.org/doi/pdf/10.1126/sciadv.aay2631},
interhash = {023c422bc0b34222f2e0439f7ed1eeaa},
intrahash = {a8e96edede4cb84ab0e8bcc011585bd9},
journal = {Science Advances},
keywords = {ak-symbolic-numeric app_physics},
number = 16,
pages = {eaay2631},
timestamp = {2024-01-22T09:30:03.000+0100},
title = {AI Feynman: A physics-inspired method for symbolic regression},
url = {https://www.science.org/doi/abs/10.1126/sciadv.aay2631},
volume = 6,
year = 2020
}