• DOI:10.48550/arXiv.2207.00283
• Corpus ID: 250243853

Learning Lattice Quantum Field Theories with Equivariant Continuous Flows

@article{Gerdes2022LearningLQ,
  title={Learning Lattice Quantum Field Theories with Equivariant Continuous Flows},
  author={Mathis Gerdes and Pim de Haan and Corrado Rainone and Roberto Bondesan and Miranda C N Cheng},
  journal={ArXiv},
  year={2022},
  volume={abs/2207.00283}
}

• Mathis Gerdes, P. D. Haan, +2 authors Miranda C N Cheng
• Published 1 July 2022
• Computer Science
• ArXiv

We propose a novel machine learning method for sampling from the high-dimensional probability distributions of Lattice Quantum Field Theories. Instead of the deep architectures used so far for this task, our proposal is based on a single neural ODE layer and incorporates the full symmetries of the problem. We test our model on the φ 4 theory, showing that it systematically outperforms previously proposed flow-based methods in sampling efficiency, and the improvement is especially pronounced for larger lattices. Compared to the previous baseline model, we improve a key metric, the effective sample size, from 1% to 91% on a lattice of size 32 × 32. We also demonstrate that our model can successfully learn a continuous family of theories at once, and the results of learning can be transferred to larger lattices. Such generalization capacities further accentuate the potential advantages of machine learning methods compared to traditional MCMC-based methods.