Machine Phenomenology: A Simple Equation Classifying Fast Radio Bursts

TL;DR

This paper presents a human-guided machine learning framework that derives a simple, physically meaningful equation classifying fast radio bursts into two categories, demonstrating the integration of human reasoning with AI for scientific discovery.

Contribution

It introduces a novel workflow combining feature selection, dimensional analysis, and symbolic regression guided by human insight to discover empirical laws from observational data.

Findings

Derived an equation classifying FRBs into two Gaussian-distributed classes

The equation remains consistent across different catalogs, indicating robustness

Framework applicable to various scientific domains

Abstract

This work shows how human physical reasoning can guide machine-driven symbolic regression toward discovering empirical laws from observations. As an example, we derive a simple equation that classifies fast radio bursts (FRBs) into two distinct Gaussian distributions, indicating the existence of two physical classes. This human-AI workflow integrates feature selection, dimensional analysis, and symbolic regression: deep learning first analyzes CHIME Catalog 1 and identifies six independent parameters that collectively provide a complete description of FRBs; guided by Buckingham-$\pi$ analysis and correlation analysis, humans then construct dimensionless groups; finally, symbolic regression performed by the machine discovers the governing equation. When applied to the newer CHIME Catalog, the equation produces consistent results, demonstrating that it captures the underlying physics. This framework is applicable to a broad range of scientific domains.