Evolving scientific discovery by unifying data and background knowledge with AI Hilbert

Ryan Cory-Wright (), Cristina Cornelio, Sanjeeb Dash, Bachir El Khadir and Lior Horesh
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Ryan Cory-Wright: Imperial College Business School
Cristina Cornelio: Samsung AI
Sanjeeb Dash: IBM Thomas J. Watson Research Center
Bachir El Khadir: IBM Thomas J. Watson Research Center
Lior Horesh: IBM Thomas J. Watson Research Center

Nature Communications, 2024, vol. 15, issue 1, 1-14

Abstract: Abstract The discovery of scientific formulae that parsimoniously explain natural phenomena and align with existing background theory is a key goal in science. Historically, scientists have derived natural laws by manipulating equations based on existing knowledge, forming new equations, and verifying them experimentally. However, this does not include experimental data within the discovery process, which may be inefficient. We propose a solution to this problem when all axioms and scientific laws are expressible as polynomials and argue our approach is widely applicable. We model notions of minimal complexity using binary variables and logical constraints, solve polynomial optimization problems via mixed-integer linear or semidefinite optimization, and prove the validity of our scientific discoveries in a principled manner using Positivstellensatz certificates. We demonstrate that some famous scientific laws, including Kepler’s Law of Planetary Motion and the Radiated Gravitational Wave Power equation, can be derived in a principled manner from axioms and experimental data.

Date: 2024
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DOI: 10.1038/s41467-024-50074-w

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