Rediscovery of Numerical Lüscher's Formula from Neural Network Training on Lattice QCD Spectra and Scattering Phase Shifts

Temel Kavramlar

The neural network can remarkably reproduce the numerical Lüscher's formula, which relates the finite-volume energy levels in lattice QCD to the infinite-volume scattering phase shifts, demonstrating the potential of data-driven approaches to uncover model-independent physical principles.

Özet

The authors present a study where they train a neural network to predict the finite-volume energy levels in lattice QCD from the infinite-volume scattering phase shifts. They find that the neural network can effectively reproduce the numerical form of Lüscher's formula, which provides a model-independent relation between these two quantities.
The key steps are:

They generate training and test data using a Hamiltonian Effective Field Theory (HEFT) model, which allows them to compute both the finite-volume spectra and the infinite-volume phase shifts.

They design a small feed-forward neural network with "SoftPlus" activation function to perform the task of predicting the finite-volume energy levels from the phase shifts.

The neural network is able to capture the model-independent features of the Lüscher's formula, even when tested on data from a different HEFT model. This is evidenced by the systematic underestimation of the energy levels compared to the model predictions, which aligns with the finite-volume corrections to Lüscher's formula.

Further tests with constant phase shifts reveal a subtle issue related to the periodicity of the phase shift, which the neural network handles by making a soft transition between the neighboring Lüscher's formula curves.

The authors conclude that the neural network has effectively rediscovered the numerical form of Lüscher's formula, demonstrating the potential of data-driven approaches to extract model-independent physical principles from intricate data.

İstatistikler

The finite-volume energy levels E(L) are systematically lower than the model predictions, indicating the neural network is capturing the finite-volume corrections to Lüscher's formula.

Alıntılar

"The neural network can remarkably reproduce the numerical Lüscher's formula to a high precision."
"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."

Önemli Bilgiler Şuradan Elde Edildi

Rediscovery of Numerical Lüscher's Formula from the Neural Network

by Yu Lu,Yi-Jia... : arxiv.org 04-09-2024

https://arxiv.org/pdf/2210.02184.pdf

Daha Derin Sorular

How can the neural network approach be extended to extract model-independent relations in more complex multi-channel scattering processes, where Lüscher's formula has limitations

In more complex multi-channel scattering processes where Lüscher's formula has limitations, the neural network approach can be extended by incorporating additional input features related to the multi-channel interactions. By including data from various channels and their corresponding phase shifts, the neural network can learn the underlying patterns and relationships that govern the scattering processes.
One approach could involve training the neural network on a dataset that includes phase shifts and energy spectra from multiple channels simultaneously. This would allow the network to capture the interplay between different channels and extract model-independent relations that govern the overall scattering behavior. Additionally, techniques such as attention mechanisms or graph neural networks could be employed to model the interactions between different channels more effectively.
By training the neural network on a diverse dataset that encompasses the complexities of multi-channel scattering, it can learn to generalize across different channels and extract underlying principles that are independent of specific models or assumptions. This data-driven approach can help uncover hidden connections and provide insights into the fundamental physics governing multi-channel scattering processes.

Can the neural network discover other model-independent principles in lattice QCD beyond the Lüscher's formula

Beyond Lüscher's formula, the neural network approach in lattice QCD can potentially discover other model-independent principles that govern the behavior of hadronic systems. One area of interest could be the study of resonance properties and decay processes in lattice QCD simulations. By training the neural network on data related to resonance states, decay channels, and scattering amplitudes, it could uncover universal relationships that hold across different resonance systems.
Furthermore, the neural network could be applied to investigate the properties of exotic hadrons, such as tetraquarks or pentaquarks, whose structures and interactions are not well understood. By analyzing the data from lattice QCD simulations of these exotic hadrons, the neural network could potentially reveal hidden symmetries, conservation laws, or other model-independent principles that govern their behavior.
Overall, the data-driven approach using neural networks in lattice QCD has the potential to uncover a wide range of model-independent principles beyond Lüscher's formula, shedding light on the underlying physics of hadronic systems and exotic particles.

What other areas of physics could benefit from similar data-driven approaches to uncover hidden model-independent structures

Various areas of physics could benefit from similar data-driven approaches to uncover hidden model-independent structures. One such area is cosmology, where neural networks could be used to analyze large datasets from cosmic microwave background radiation, galaxy surveys, and gravitational wave observations. By training neural networks on cosmological data, researchers could potentially discover new relationships between cosmological parameters, dark matter properties, and the expansion of the universe.
In particle physics, neural networks could aid in the analysis of collider data to uncover new physics beyond the Standard Model. By examining particle collision events and detector outputs, neural networks could identify patterns indicative of new particles, interactions, or symmetries that are not predicted by existing models.
Moreover, in condensed matter physics, neural networks could be utilized to study complex materials and phase transitions. By analyzing experimental data on material properties, electronic structures, and phase diagrams, neural networks could reveal hidden correlations, emergent phenomena, and novel quantum states that defy conventional theoretical descriptions.
Overall, data-driven approaches using neural networks have the potential to revolutionize various fields of physics by uncovering hidden model-independent structures, providing new insights, and guiding future research directions.