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

Nature Reviews Physics volume 5, pages 526–535 (2023)Cite this article

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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.

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Fig. 1: Depiction of a single cube within the spacetime lattice of a lattice QCD calculation.
Fig. 2: Comparison between the sampling tasks of quantum field generation for lattice quantum chromodynamics and image generation.
Fig. 3: Illustration of a gauge-equivariant transformation layer80, 81.
Fig. 4: Demonstration of the advantages of flow-based sampling in a U(1) lattice gauge theory in two spacetime dimensions83.
Fig. 5: Sketch of the upfront and sampling costs of hybrid Monte Carlo compared with flow-based models.

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Acknowledgements

We thank W. Detmold and R. D. Young for comments on the manuscript. P.E.S. was supported in part by the US Department of Energy, Office of Science, Office of Nuclear Physics, under grant contract number DE-SC0011090, and by Early Career Award DE-SC0021006, by a NEC research award, and by the Carl G. and Shirley Sontheimer Research Fund. G.K. was supported by funding from the Schweizerischer Nationalfonds (grant agreement no. 200020_200424).

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Authors and Affiliations

  1. Physics Department, University of Wisconsin-Madison, Madison, WI, USA

    Kyle Cranmer

  2. Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Bern, Switzerland

    Gurtej Kanwar

  3. Google DeepMind, London, UK

    Sébastien Racanière & Danilo J. Rezende

  4. Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Phiala E. Shanahan

  5. The NSF AI Institute for Artificial Intelligence and Fundamental Interactions, Cambridge, MA, USA

    Phiala E. Shanahan

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Cranmer, K., Kanwar, G., Racanière, S. et al. Advances in machine-learning-based sampling motivated by lattice quantum chromodynamics. Nat Rev Phys 5, 526–535 (2023). https://doi.org/10.1038/s42254-023-00616-w

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