A Monte Carlo estimator of flow fields for sampling and noise problems

2026-02-27

AI Summary

This work addresses the challenges of critical slowing down and poor signal-to-noise ratios in lattice field theory by proposing a flow-based field transformation method. By introducing a Monte Carlo estimator coupled with Langevin noise into an annealing sequence of distributions, the approach efficiently estimates the normalizing flow, which can then be used either for direct sampling or to generate unbiased training data for machine learning models. The estimator substantially suppresses statistical noise in the flow integration, thereby enhancing sampling efficiency. Numerical experiments on U(1) transport problems and SU(N) glueball correlators demonstrate that the proposed method significantly improves both signal-to-noise ratios and sampling performance, offering a promising new avenue for efficient simulations in lattice field theory.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Learned field transformations may help address ubiquitous critical slowing down and signal-to-noise problems in lattice field theory. In the context of an annealed sequence of distributions, field transformations are defined by integrating flow fields that exactly solve a local transport problem. These proceedings discuss a new Monte Carlo approach to evaluating these flow fields, which can then be used directly in such contexts or as a means of generating unbiased training data for machine learning approaches. By defining the Monte Carlo estimator using coupled Langevin noise, the statistical noise in the required integrals is significantly mitigated. Demonstrations of the method include a U(1) transport problem and an SU(N) glueball correlator.

Problem

• critical slowing down
• signal-to-noise problem
• lattice field theory
• flow fields
• Monte Carlo estimator

Innovation

• Monte Carlo estimator
• flow fields
• coupled Langevin noise
• critical slowing down
• lattice field theory