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

Aug 3, 2026

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Sampling from known probability distributions underpins computational work across scientific disciplines, and generative machine-learning (ML) has shown strong promise for similar tasks such as image, text, and audio generation. Scientific settings, however, introduce distinctive constraints, including complex symmetries and the need for exactness guarantees. This Perspective reviews advances in ML-based sampling driven by lattice quantum field theory, focusing on quantum chromodynamics, where supercomputing costs are substantial and scaling ML architectures to leading facilities remains challenging yet potentially transformative for first-principles physics.

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Abstract

1 Introduction

arXiv :2309 .0 1 156v 1 [hep-lat] 3 Sep 2023 Advances in machine-learning-based sampling motivated by lattice quantum chromodynamics Kyle Cranmer 1 , Gurtej Kanwar2 , Sbastien Racanire3 , Danilo J. Rezende3 , and Phiala E. Shanahan4,5,* 1 Physics Department, University of Wisconsin-Madison, Madison, WI, USA 2Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Bern, Switzerland 3 Google DeepMind, London, UK 4 Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, USA 5The NSF AI Institute for Artificial Intelligence and Fundamental Interactions, Cambridge, MA, USA * e-mail: [pshana@mit.edu](pshana@mit.edu) 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 advancesin 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. 1 Introduction Theoretical nuclear physics has the ironic feature that although the fundamental laws are well understood, the computations required to make quantitative, first-principles predictions are in many cases currently infeasible. The strong nuclear force is fundamentally described by the quantum field theory known as Quantum Chromodynamics (QCD), which details the dynamics of constituent particles—quarks and gluons—that arise as excitations of underlying quantum fields. This theory successfully predicts a wide range of phenomena that occur at different energy scales, ranging from the high-energy collisions at the Large Hadron Collider to the properties and interactions of composite particles such as the proton and neutron, as well as the nuclei they form. At high energies, the interactions between quarks and gluons are weak, and accurate QCD calculations can be made using a perturbative expansion, which is often represented with Feynman diagrams. At the lower energies relevant for much of nuclear physics, the interactions between quarks and gluons are strong and the perturbative approach breaks down. In this regime, quantitative predictions can be achieved through a computational approach known as lattice QCD, in which the quark and gluon fields are represented on a discrete spacetime lattice. Many key aspects of nuclear physics can be computed precisely in this framework. For example, such calculations reveal how the masses of the proton and neutron arise from the fundamental quarks and gluons 1 , and they have been used to make predictions of the masses of new composite particles later discovered by experiments at CERN2–4. However, the reach of this approach is limited by its computational cost, and controlled first-principles QCD calculation

FAQs

Why is sampling a critical challenge in lattice QCD calculations?

Lattice QCD requires estimating statistical averages over highly structured, high-dimensional, multi-modal distributions of quark and gluon field configurations, making Monte Carlo sampling computationally difficult.

How does generative machine learning relate to sampling tasks in scientific domains?

Generative ML models can build on success in data generation tasks (image, text, audio) and may address sampling, but scientific applications often require exactness guarantees and must respect domain-specific structure such as symmetries.

What does the Perspective emphasize as the key benefit of reducing computational cost in lattice field theory?

Lower costs would enable more controlled first-principles calculations, supporting quantitative studies of particle, nuclear, and condensed matter physics that are currently intractable, including investigations tied to fundamental parameters and element formation.

Aug 3, 2026

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