Combining complex Langevin dynamics with score-based and energy-based diffusion models

Abstract

Theories with a sign problem due to a complex action or Boltzmann weight can sometimes be numerically solved using a stochastic process in the complexified configuration space. However, the probability distribution effectively sampled by this complex Langevin process is not known a priori and notoriously hard to understand. In generative AI, diffusion models can learn distributions, or their log derivatives, from data. We explore the ability of diffusion models to learn the distributions sampled by a complex Langevin process, comparing score-based and energy-based diffusion models, and speculate about possible applications.

22 pages, many figures

References in corpus (34)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• High density QCD on a Lefschetz thimble?
• The Complex Langevin method: When can it be trusted?
• Simulating full QCD at nonzero density using the complex Langevin equation
• Complex Langevin: Etiology and Diagnostics of its Main Problem
• Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential
• Gauge cooling in complex Langevin for QCD with heavy quarks
• Introductory lectures on lattice QCD at nonzero baryon number
• Stochastic quantization at finite chemical potential
• New insights into the problem with a singular drift term in the complex Langevin method
• Complex Langevin dynamics in the SU(3) spin model at nonzero chemical potential revisited
• Real-time gauge theory simulations from stochastic quantization with optimized updating
• Stability of complex Langevin dynamics in effective models
• Lefschetz thimbles and stochastic quantisation: Complex actions in the complex plane
• Complex Langevin dynamics at finite chemical potential: mean field analysis in the relativistic Bose gas
• On the convergence of complex Langevin dynamics: the three-dimensional XY model at finite chemical potential
• Complex Langevin and boundary terms
• Localised distributions and criteria for correctness in complex Langevin dynamics
• The QCD phase diagram in the limit of heavy quarks using complex Langevin dynamics
• Controlling Complex Langevin simulations of lattice models by boundary term analysis
• Calculating the EoS of the dense quark-gluon plasma using the Complex Langevin equation
• Complex Probabilities on R^N as Real Probabilities on C^N and an Application to Path Integrals
• Diffusion Models as Stochastic Quantization in Lattice Field Theory
• Deconfinement transition line with the Complex Langevin equation up to $\mu /T\sim 5$
• Complex Langevin calculations in QCD at finite density
• Stabilizing complex Langevin for real-time gauge theories with an anisotropic kernel
• Towards learning optimized kernels for complex Langevin
• Schwinger-Dyson equations and line integrals
• On learning higher-order cumulants in diffusion models
• Real-time correlators in 3+1D thermal lattice gauge theory
• Stochastic quantization and diffusion models
• Lefschetz thimble-inspired weight regularizations for complex Langevin simulations
• Necessary and sufficient conditions for correctness of complex Langevin
• On the validity of the complex Langevin method near the deconfining phase transition in QCD at finite density