A JEPA-based hypernetwork maps lattice field theory couplings to flow-model weights, and the geometry of those weights recovers the phase transition, intrinsic dimension, and Ising critical exponent of 2D scalar field theory without supervised physics labels.
Kanwar, Flow-based sampling for lattice field theories, in40th International Symposium on Lattice Field Theory (2024) arXiv:2401.01297 [hep-lat]
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abstract
Critical slowing down and topological freezing severely hinder Monte Carlo sampling of lattice field theories as the continuum limit is approached. Recently, significant progress has been made in applying a class of generative machine learning models, known as "flow-based" samplers, to combat these issues. These generative samplers also enable promising practical improvements in Monte Carlo sampling, such as fully parallelized configuration generation. These proceedings review the progress towards this goal and future prospects of the method.
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A coupling-flow global proposal for Monte Carlo sampling in 2D pure SU(2) lattice gauge theory is shown to be formally valid and to reproduce the target ensemble in proof-of-principle tests, with modest hybrid gains but no clear outperformance over local baselines.
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.
Normalizing flows enable all-order QED corrections in lattice scalar QED in 2-4 dimensions with reduced variance and transferability from small to large lattices.
Implicit score matching trains diffusion models that successfully sample SU(3) Wilson gauge configurations on lattices, with a Hamiltonian-dynamics corrector needed for strong coupling.
Metadynamics bias potentials and volume-extrapolation strategies reduce integrated autocorrelation times of topological charge in lattice gauge theories.
Reviews approaches such as Lefschetz thimbles, complex Langevin dynamics, dual variables, tensor renormalization group, and machine learning to control the sign problem in lattice field theories.
citing papers explorer
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Weight-Space Physics: Interpretable Hypernetworks for Lattice Quantum Field Theories
A JEPA-based hypernetwork maps lattice field theory couplings to flow-model weights, and the geometry of those weights recovers the phase transition, intrinsic dimension, and Ising critical exponent of 2D scalar field theory without supervised physics labels.
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Flow-Based Global Proposals for Monte Carlo Sampling in SU(2) Lattice Gauge Theory
A coupling-flow global proposal for Monte Carlo sampling in 2D pure SU(2) lattice gauge theory is shown to be formally valid and to reproduce the target ensemble in proof-of-principle tests, with modest hybrid gains but no clear outperformance over local baselines.
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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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Normalizing flows for all-orders QED corrections in lattice field theory
Normalizing flows enable all-order QED corrections in lattice scalar QED in 2-4 dimensions with reduced variance and transferability from small to large lattices.
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Diffusion model for SU(N) gauge theories
Implicit score matching trains diffusion models that successfully sample SU(3) Wilson gauge configurations on lattices, with a Hamiltonian-dynamics corrector needed for strong coupling.
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Enhanced Sampling Techniques for Lattice Gauge Theory
Metadynamics bias potentials and volume-extrapolation strategies reduce integrated autocorrelation times of topological charge in lattice gauge theories.
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Lattice field theories with a sign problem
Reviews approaches such as Lefschetz thimbles, complex Langevin dynamics, dual variables, tensor renormalization group, and machine learning to control the sign problem in lattice field theories.