Advances in machine-learning-based sampling motivated by lattice quantum chromodynamics

Abstract

Sampling from known probability distributions is a ubiquitous task in computational science, underlying calculations in domains from linguistics to biology and physics. Generative machine-learning (ML) models have emerged as a promising tool in this space, building on the success of this approach in applications such as image, text, and audio generation. Often, however, generative tasks in scientific domains have unique structures and features -- such as complex symmetries and the requirement of exactness guarantees -- that present both challenges and opportunities for ML. This Perspective outlines the advances in ML-based sampling motivated by lattice quantum field theory, in particular for the theory of quantum chromodynamics. Enabling calculations of the structure and interactions of matter from our most fundamental understanding of particle physics, lattice quantum chromodynamics is one of the main consumers of open-science supercomputing worldwide. The design of ML algorithms for this application faces profound challenges, including the necessity of scaling custom ML architectures to the largest supercomputers, but also promises immense benefits, and is spurring a wave of development in ML-based sampling more broadly. In lattice field theory, if this approach can realize its early promise it will be a transformative step towards first-principles physics calculations in particle, nuclear and condensed matter physics that are intractable with traditional approaches.

arXiv comment11 pages, 5 figures

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• Numerical determination of the width and shape of the effective string using Stochastic Normalizing Flows
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• On learning higher-order cumulants in diffusion models
• Scaling of Stochastic Normalizing Flows in $\mathrm{SU}(3)$ lattice gauge theory
• Rényi entanglement entropy of spin chain with Generative Neural Networks
• Flow-Based Sampling for Entanglement Entropy and the Machine Learning of Defects
• Ultra fast, event-by-event heavy-ion simulations for next generation experiments
• Bayesian RG Flow in Neural Network Field Theories
• Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
• Phase diagram and eigenvalue dynamics of stochastic gradient descent in multilayer neural networks
• A comparative lattice analysis of $SU(2)$ dark gluebal
• Global sampling of Feynman's diagrams through Normalizing Flow
• Applications of flow models to the generation of correlated lattice QCD ensembles
• Group-Equivariant Diffusion Models for Lattice Field Theory