AI Feynman: a Physics-Inspired Method for Symbolic Regression
This addresses the problem of automating the discovery of symbolic expressions from data for researchers in physics and AI, representing a significant advance over prior methods.
The paper tackles symbolic regression by developing a physics-inspired recursive algorithm that combines neural networks with techniques leveraging symmetries and other properties, achieving 100% success on a benchmark set of 100 equations from the Feynman Lectures and improving state-of-the-art success rates from 15% to 90% on a more difficult test set.
A core challenge for both physics and artificial intellicence (AI) is symbolic regression: finding a symbolic expression that matches data from an unknown function. Although this problem is likely to be NP-hard in principle, functions of practical interest often exhibit symmetries, separability, compositionality and other simplifying properties. In this spirit, we develop a recursive multidimensional symbolic regression algorithm that combines neural network fitting with a suite of physics-inspired techniques. We apply it to 100 equations from the Feynman Lectures on Physics, and it discovers all of them, while previous publicly available software cracks only 71; for a more difficult test set, we improve the state of the art success rate from 15% to 90%.