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Physical Review D

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Learning trivializing gradient flows for lattice gauge theories

Simone Bacchio1, Pan Kessel2,3, Stefan Schaefer4, and Lorenz Vaitl2

  • 1Computation-based Science and Technology Research Center, The Cyprus Institute, Nicosia, Cyprus
  • 2Machine Learning Group, Technische Universität Berlin, Berlin, Germany
  • 3BIFOLD Berlin Institute for the Foundations of Learning and Data, Berlin, Germany
  • 4John von Neumann-Institut für Computing NIC, Deutsches Elektronen-Synchrotron DESY, Germany

Lecture notes on normalizing flows for lattice quantum field theories

Miranda C. N. Cheng and Niki Stratikopoulou

SciPost Phys. Lect. Notes 110 (2026)

Machine-Learned Renormalization-Group-Improved Gauge Actions and Classically Perfect Gradient Flows

Kieran Holland, Andreas Ipp, David I. Müller, and Urs Wenger

Phys. Rev. Lett. 136 031901 (2026)

Variance reduction in lattice QCD observables via normalizing flows

Ryan Abbott, Denis Boyda, Yang Fu, Daniel C. Hackett, Gurtej Kanwar, Fernando Romero-López, Phiala E. Shanahan, and Julian M. Urban

Phys. Rev. D 114 014513 (2026)

FLAG review 2024

Y. Aoki et al.

Phys. Rev. D 113 014508 (2026)

Scaling flow-based approaches for topology sampling in SU(3) gauge theory

Claudio Bonanno, Andrea Bulgarelli, Elia Cellini, Alessandro Nada, Dario Panfalone, Davide Vadacchino, and Lorenzo Verzichelli

J. High Energ. Phys. 2026 51 (2026)

Nonperturbative trivializing flows for lattice gauge theories

Mathis Gerdes, Pim de Haan, Roberto Bondesan, and Miranda C. N. Cheng

Phys. Rev. D 112 094516 (2025)

Gauge covariant neural network for quarks and gluons

Yuki Nagai and Akio Tomiya

Phys. Rev. D 111 074501 (2025)

Scaling of stochastic normalizing flows in SU(3) lattice gauge theory

Andrea Bulgarelli, Elia Cellini, and Alessandro Nada

Phys. Rev. D 111 074517 (2025)

Stochastic automatic differentiation and the signal to noise problem

G. Catumba and A. Ramos

Eur. Phys. J. C 85 1037 (2025)

Gauge-equivariant pooling layers for preconditioners in lattice QCD

C. Lehner and T. Wettig

Phys. Rev. D 110 034517 (2024)

Machine learning a fixed point action for SU(3) gauge theory with a gauge equivariant convolutional neural network

Kieran Holland, Andreas Ipp, David I. Müller, and Urs Wenger

Phys. Rev. D 110 074502 (2024)

Nucleon axial and pseudoscalar form factors using twisted-mass fermion ensembles at the physical point

Constantia Alexandrou, Simone Bacchio, Martha Constantinou, Jacob Finkenrath, Roberto Frezzotti, Bartosz Kostrzewa, Giannis Koutsou, Gregoris Spanoudes, and Carsten Urbach

Phys. Rev. D 109 034503 (2024)

Applications of flow models to the generation of correlated lattice QCD ensembles

Ryan Abbott, Aleksandar Botev, Denis Boyda, Daniel C. Hackett, Gurtej Kanwar, Sébastien Racanière, Danilo J. Rezende, Fernando Romero-López, Phiala E. Shanahan, and Julian M. Urban

Phys. Rev. D 109 094514 (2024)

Parallel tempered metadynamics: Overcoming potential barriers without surfing or tunneling

Timo Eichhorn, Gianluca Fuwa, Christian Hoelbling, and Lukas Varnhorst

Phys. Rev. D 109 114504 (2024)

Sampling the lattice Nambu-Goto string using Continuous Normalizing Flows

Michele Caselle, Elia Cellini, and Alessandro Nada

J. High Energ. Phys. 2024 48 (2024)

Diffusion models as stochastic quantization in lattice field theory

L. Wang, G. Aarts, and K. Zhou

J. High Energ. Phys. 2024 60 (2024)

Study of the topological quantities of lattice QCD using a modified DCGAN frame

Lin 璘 Gao 高, Heping 和平 Ying 应, and Jianbo 剑波 Zhang 张

Chinese Phys. C 48 053111 (2024)

Learning lattice quantum field theories with equivariant continuous flows

Mathis Gerdes, Pim de Haan, Corrado Rainone, Roberto Bondesan, and Miranda C. N. Cheng

SciPost Phys. 15 238 (2023)

Gauge-equivariant neural networks as preconditioners in lattice QCD

C. Lehner and T. Wettig

Phys. Rev. D 108 034503 (2023)

Sampling U(1) gauge theory using a retrainable conditional flow-based model

Ankur Singha, Dipankar Chakrabarti, and Vipul Arora

Phys. Rev. D 108 074518 (2023)

Detecting and mitigating mode-collapse for flow-based sampling of lattice field theories

Kim A. Nicoli, Christopher J. Anders, Tobias Hartung, Karl Jansen, Pan Kessel, and Shinichi Nakajima

Phys. Rev. D 108 114501 (2023)

Novel approach for computing gradients of physical observables

Simone Bacchio

Phys. Rev. D 108 L091508 (2023)

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

Kyle Cranmer, Gurtej Kanwar, Sébastien Racanière, Danilo J. Rezende, and Phiala E. Shanahan

Nat Rev Phys 5 526 (2023)

Learning trivializing flows

D. Albandea, L. Del Debbio, P. Hernández, R. Kenway, J. MarshRossney, and A. Ramos

Eur. Phys. J. C 83 676 (2023)

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