Rediscovery of Numerical L\"uscher's Formula from the Neural Network

TL;DR

This paper demonstrates that neural networks can accurately reproduce L"uscher's formula, revealing its model-independent nature and showcasing the potential of data-driven methods to uncover fundamental physical relations.

Contribution

The study rediscoveres L"uscher's formula using neural networks, highlighting their ability to capture model-independent physical relations from data.

Findings

Neural networks can predict the spectrum from phase shifts with high precision.

The model reproduces L"uscher's formula, confirming its model-independent property.

The approach suggests neural networks' potential in discovering underlying physical principles.

Abstract

We present that by predicting the spectrum in discrete space from the phase shift in continuous space, the neural network can remarkably reproduce the numerical L\"uscher's formula to a high precision. The model-independent property of the L\"uscher's formula is naturally realized by the generalizability of the neural network. This exhibits the great potential of the neural network to extract model-independent relation between model-dependent quantities, and this data-driven approach could greatly facilitate the discovery of the physical principles underneath the intricate data.