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

Author

Listed:
  • Cristina Cornelio

    (IBM Research—Mathematics and Theoretical Computer Science
    Samsung AI—Machine Learning and Data Intelligence)

  • Sanjeeb Dash

    (IBM Research—Mathematics and Theoretical Computer Science)

  • Vernon Austel

    (IBM Research—Mathematics and Theoretical Computer Science)

  • Tyler R. Josephson

    (University of Maryland
    University of Minnesota)

  • 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
    Columbia University, Computer Science)

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.

Suggested Citation

  • Cristina Cornelio & Sanjeeb Dash & Vernon Austel & Tyler R. Josephson & Joao Goncalves & Kenneth L. Clarkson & Nimrod Megiddo & Bachir El Khadir & Lior Horesh, 2023. "Combining data and theory for derivable scientific discovery with AI-Descartes," Nature Communications, Nature, vol. 14(1), pages 1-10, December.
    • Handle: RePEc:nat:natcom:v:14:y:2023:i:1:d:10.1038_s41467-023-37236-y
    DOI: 10.1038/s41467-023-37236-y
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    Cited by:

    1. Wonho Zhung & Hyeongwoo Kim & Woo Youn Kim, 2024. "3D molecular generative framework for interaction-guided drug design," Nature Communications, Nature, vol. 15(1), pages 1-12, December.
    2. Ryan Cory-Wright & Cristina Cornelio & Sanjeeb Dash & Bachir El Khadir & Lior Horesh, 2024. "Evolving scientific discovery by unifying data and background knowledge with AI Hilbert," Nature Communications, Nature, vol. 15(1), pages 1-14, December.

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