AI Article Synopsis
- The goal of science is to find simple scientific formulas that explain natural phenomena and fit with current theories, often through manipulating existing equations and verifying them with experiments.
- The proposed method aims to improve this process by representing scientific laws as polynomials, using binary variables and logical constraints to solve complex optimization problems.
- The approach successfully derives well-known scientific laws like Kepler's Law and the Radiated Gravitational Wave Power equation, while ensuring that discoveries are backed by both axioms and experimental data.
Article 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.
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|---|---|
| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC11247103 | PMC |
| http://dx.doi.org/10.1038/s41467-024-50074-w | DOI Listing |
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