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Abstract

For centuries, scientists have attempted to identify and document analytical laws that underlie physical phenomena in nature. Despite the prevalence of computing power, the process of finding natural laws and their corresponding equations has resisted automation. A key challenge to finding analytic relations automatically is defining algorithmically what makes a correlation in observed data important and insightful. We propose a principle for the identification of nontriviality. We demonstrated this approach by automatically searching motion-tracking data captured from various physical systems, ranging from simple harmonic oscillators to chaotic double-pendula. Without any prior knowledge about physics, kinematics, or geometry, the algorithm discovered Hamiltonians, Lagrangians, and other laws of geometric and momentum conservation. The discovery rate accelerated as laws found for simpler systems were used to bootstrap explanations for more complex systems, gradually uncovering the “alphabet” used to describe those systems.
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Supplementary Material

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File (invar_datasets.zip)
File (schmidt.som.pdf)

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This research was supported in part by Integrative Graduate Education and Research Traineeship program in nonlinear systems, a U.S. NSF graduate research fellowship, and NSF Creative-IT grant 0757478 and CAREER grant 0547376. We thank M. Kurman for editorial consultation and substantive editing of the manuscript.

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Published In

Science
Volume 324 | Issue 5923
3 April 2009

Submission history

Received: 15 September 2008
Accepted: 19 February 2009
Published in print: 3 April 2009

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Authors

Affiliations

Michael Schmidt
Computational Biology, Cornell University, Ithaca, NY 14853, USA.
Hod Lipson*
School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA.
Computing and Information Science, Cornell University, Ithaca, NY 14853, USA.

Notes

* To whom correspondence should be addressed. E-mail: [email protected]

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