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

Cristina Cornelio (), Sanjeeb Dash, Vernon Austel, Tyler R. Josephson, Joao Goncalves, Kenneth L. Clarkson, Nimrod Megiddo, Bachir El Khadir and Lior Horesh ()
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Cristina Cornelio: IBM Research—Mathematics and Theoretical Computer Science
Sanjeeb Dash: IBM Research—Mathematics and Theoretical Computer Science
Vernon Austel: IBM Research—Mathematics and Theoretical Computer Science
Tyler R. Josephson: University of Maryland
Joao Goncalves: IBM Research—Mathematics and Theoretical Computer Science
Kenneth L. Clarkson: IBM Research—Mathematics and Theoretical Computer Science
Nimrod Megiddo: IBM Research—Mathematics and Theoretical Computer Science
Bachir El Khadir: IBM Research—Mathematics and Theoretical Computer Science
Lior Horesh: IBM Research—Mathematics and Theoretical Computer Science

Nature Communications, 2023, vol. 14, issue 1, 1-10

Abstract: 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.

Date: 2023
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Citations: View citations in EconPapers (3)

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DOI: 10.1038/s41467-023-37236-y

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