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

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.