Rediscovery of Numerical Lüscher's Formula from the Neural Network
This work addresses the challenge of deriving model-independent physical relations from complex data, which could facilitate discoveries in physics, though it appears incremental as it applies an existing neural network approach to a known formula.
The researchers tackled the problem of reproducing the numerical Lüscher's formula, a model-independent relation in physics, by using a neural network to predict spectra from phase shifts with high precision. The result demonstrated the neural network's ability to accurately extract this formula, showcasing its potential for data-driven discovery of physical principles.
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 Lüscher's formula to a high precision. The model-independent property of the Lüscher'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.