Combining data and theory for derivable scientific discovery with AI-Descartes

Abstract Scientists aim to discover meaningful formulae that accurately describe experimental data. Mathematical models of natural phenomena can be manually created from domain knowledge and fitted to data, or, in contrast, created automatically from large datasets with machine-learning algorithms....

Full description

Saved in:
Bibliographic Details
Published in:Nature communications 2023-04, Vol.14 (1)
Main Authors: Cornelio, Cristina, Dash, Sanjeeb, Austel, Vernon, Josephson, Tyler R., Goncalves, Joao, Clarkson, Kenneth L., Megiddo, Nimrod, El Khadir, Bachir, Horesh, Lior
Format: Article
Language:English
Subjects:
Science & Technology - Other Topics
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Abstract Scientists aim to discover meaningful formulae that accurately describe experimental data. Mathematical models of natural phenomena can be manually created from domain knowledge and fitted to data, or, in contrast, created automatically from large datasets with machine-learning algorithms. The problem of incorporating prior knowledge expressed as constraints on the functional form of a learned model has been studied before, while finding models that are consistent with prior knowledge expressed via general logical axioms is an open problem. We develop a method to enable principled derivations of models of natural phenomena from axiomatic knowledge and experimental data by combining logical reasoning with symbolic regression. We demonstrate these concepts for Kepler’s third law of planetary motion, Einstein’s relativistic time-dilation law, and Langmuir’s theory of adsorption. We show we can discover governing laws from few data points when logical reasoning is used to distinguish between candidate formulae having similar error on the data.
ISSN:2041-1723
2041-1723