Classifying Topological Charge in SU(3) Yang-Mills Theory with Machine Learning

Abstract

We apply a machine learning technique for identifying the topological charge of quantum gauge configurations in four-dimensional SU(3) Yang-Mills theory. The topological charge density measured on the original and smoothed gauge configurations with and without dimensional reduction is used as inputs for the neural networks (NN) with and without convolutional layers. The gradient flow is used for the smoothing of the gauge field. We find that the topological charge determined at a large flow time can be predicted with high accuracy from the data at small flow times by the trained NN; for example, the accuracy exceeds $99\%$ with the data at $t/a^2\le 0.3$. High robustness against the change of simulation parameters is also confirmed with a fixed physical volume. We find that the best performance is obtained when the spatial coordinates of the topological charge density are fully integrated out in preprocessing, which implies that our convolutional NN does not find characteristic structures in multi-dimensional space relevant for the determination of the topological charge.

arXiv comment28 pages, 12 figures, version to appear in PTEP

References in corpus (24)

• Adam: A Method for Stochastic Optimization
• WaveNet: A Generative Model for Raw Audio
• Searching for Exotic Particles in High-Energy Physics with Deep Learning
• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Infinite N phase transitions in continuum Wilson loop operators
• Critical slowing down and error analysis in lattice QCD simulations
• Detection of phase transition via convolutional neural network
• Axion phenomenology and $\theta$-dependence from $N_f=2+1$ lattice QCD
• Finite volume QCD at fixed topological charge
• Machine Learning of Explicit Order Parameters: From the Ising Model to SU(2) Lattice Gauge Theory
• Parton Shower Uncertainties in Jet Substructure Analyses with Deep Neural Networks
• Lattice QCD input for axion cosmology
• Equation of State for SU(3) Gauge Theory via the Energy-Momentum Tensor under Gradient Flow
• Toward solving the sign problem with path optimization method
• Non-Gaussianities in the topological charge distribution of the SU(3) Yang--Mills theory
• Topological susceptibility at high temperature on the lattice
• Lattice QCD for Cosmology
• Machine learning action parameters in lattice quantum chromodynamics
• Topological susceptibility in finite temperature (2+1)-flavor QCD using gradient flow
• ${\chi }_{\text{top}}(T\gg T_{\text{c}})$ in pure-glue QCD through reweighting
• Topological susceptibility at $T>T_{\mathrm{c}}$ from master-field simulations of the SU(3) gauge theory
• Topology in QCD and the axion abundance
• Applications of deep learning to relativistic hydrodynamics
• Featuring the topology with the unsupervised machine learning

Cited by in corpus (1)

• Machine-learning physics from unphysics: Finding deconfinement temperature in lattice Yang-Mills theories from outside the scaling window