Distilling Free-Form Natural Laws from Experimental Data
Michael Schmidt1 and
Hod Lipson2,3*
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.
2 School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA.
3 Computing and Information Science, Cornell University, Ithaca, NY 14853, USA.
* To whom correspondence should be addressed. E-mail: hod.lipson{at}cornell.edu
