Distilling Free-Form Natural Laws from Experimental Data

An interesting paper of that name came out in Science two years ago. There’s a neat video:

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.

The Eureqa application used to mine data for relationships has been released at the authors’ Cornell site.

I think an interesting question is, will this approach work on noisy or ill-defined systems like climate or organizations? My guess is that it will have the same limitations as human-produced science. There’s a reason that a lot of physical laws were nailed down centuries ago, but our models of biological, economic and social phenomena are still pretty limited.

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