Machine learning for lattice QCD

In this review I summarize how machine learning can be used in lattice gauge theory simulations and what ap-proaches are currently available to improve the sampling of gauge field configurations, with a focus on applications in four-dimensional SU(3) gauge theories. These include approaches based on generative machine-learning models such as (stochastic) normalizing flows and diffusion processes, and an approach based on renormalization group (RG) transformations, more specifically the machine learning of RG-improved gauge actions using gauge-equivariant convolutional neural networks. In particular, I present scaling results for a machine-learned fixed-point action in four-dimensional SU(3) gauge theory towards the continuum limit. The results include observables based on the classically perfect gradient-flow scales, which are free of tree-level lattice artefacts to all orders, and quantities related to the static potential and the deconfinement transition.

The generating functional in quantum field theory provides the natural framework for constructing correlation functions as derivatives with respect to source operators. We present a methodology that leverages machine-learned normalizing flows to reduce the variance of arbitrary $N$-point correlation functions of bosonic operators in lattice gauge field theory calculations by encoding a representation of the generating functional. We show that it is possible to systematically approach noiseless estimators of correlation functions in this framework. We demonstrate this methodology with applications to calculations of glueball correlation functions and Wilson loops in Quantum Chromodynamics and Yang-Mills theory. The results show up to three orders of magnitude variance reduction.

Lattice quantum chromodynamics (LQCD) provides a first-principles framework for computing hadronic observables, but its practical use remains limited by the substantial expertise required to turn research motivation into reliable computing workflows. Here we present LQCDMaster, a tool-augmented, skill-guided and domain-specialized scientific computing agent that converts natural-language LQCD research tasks into executable PyQUDA computing workflows, including measurement scripts, job-submission artifacts, execution logs and numerical outputs. The system combines agentic planning, expert-annotated LQCD skills and a deterministic Wick-contraction tool to constrain the algebraically fragile components of code generation. We evaluate LQCDMaster on a benchmark at the forefront of scientific research, comprising 70 LQCD computing tasks, with observables covering local and nonlocal two-point functions, Wilson loops, meson and baryon three-point functions. The generated workflows exactly reproduce expert-written implementations in 63 of 70 tasks at machine precision, with three additional discrepancies attributable to convention mismatches. Across representative observables, the agent reduces implementation time from hours to minutes while preserving end-to-end numerical validation. Further, we present a typical case of LQCDMaster-driven exploration: a lattice computation of light-cone distribution amplitudes with diagonal Wilson-line, a quantity accessible with standard methods but never before computed, and computation of the spectrum of proton, deuteron, triton, hyperon, hyperdeuteron and hypertriton. This work pioneers the paradigm of agentic scientific computing by automating the end-to-end scientific computing workflows in lattice QCD research, lowering its barrier and facilitating the exploration and verification of non-standard scientific ideas.