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Advances in machine-learning-based sampling motivated by lattice quantum chromodynamics
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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.
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Cited by 10 Pith papers
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Diffusion Models for Sampling Near Criticality in Lattice Field Theories
Fully convolutional diffusion models trained on small lattices transfer to unseen larger volumes for 2D/3D phi^4 sampling across phases, matching or beating same-size training on most observables.
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Solving Functional Renormalization Group Equations with Neural Networks
A neural network that learns fRG flows from the equation residual, with a large-N analytic baseline, matches finite-difference and discontinuous-Galerkin solvers for O(N) models.
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Exploring Generative Networks for Manifolds with Non-Trivial Topology
A GFlowNet-inspired diffusion sampler is proposed and shown, on toy and 2D lattice scalar models, to generate configurations across disconnected sectors that normalizing flows and plain diffusion models miss.
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Scaling of Stochastic Normalizing Flows in $\mathrm{SU}(3)$ lattice gauge theory
First demonstration that Stochastic Normalizing Flows inherit the linear-with-volume scaling of non-equilibrium MCMC in 4D SU(3) lattice gauge theory, with a factor-of-two efficiency gain.
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Studying Effective String Theory using deep generative models
Flow-based samplers numerically confirm the next-to-leading-order width and the resummed string-tension conjecture for the Nambu-Goto effective string in 2+1 dimensions.
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Diffusion models and stochastic quantisation in lattice field theory
Diffusion models, whose backward denoising step resembles stochastic quantisation, can learn from HMC data to generate configurations for 2D scalar lattice field theory.
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Physics-Driven Learning for Inverse Problems in Quantum Chromodynamics
A perspective article reviewing physics-driven machine learning for inverse problems in QCD, without introducing new data, derivations, or quantitative results.
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