Distilling Free-Form Natural Laws from Experimental Data

TLDR

Scientists have long sought analytical laws governing natural phenomena, but automating their discovery remains difficult because defining algorithmically what makes a data correlation meaningful is challenging. The authors propose a principle for identifying nontrivial relationships in data. They apply this principle to automatically search motion‑tracking data from various physical systems, using discovered laws to bootstrap more complex ones. The algorithm uncovered Hamiltonians, Lagrangians, and conservation laws without prior physics knowledge, and its discovery rate accelerated as simpler systems informed more complex ones.

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.