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Performance of machine-learning-assisted Monte Carlo in sampling from simple statistical physics models
Luca Maria Del Bono1,2, Federico Ricci-Tersenghi1,2,3, Francesco Zamponi1
1Sapienza Università di Roma, Dipartimento di Fisica, Piazzale Aldo Moro 5, Rome 00185, Italy.
Physical Review. E
|November 18, 2025
Summary
Machine learning aids hard-to-sample simulations. This study analyzes global annealing with a MADE architecture for the Curie-Weiss model, offering theoretical insights for Monte Carlo sampling optimization.
Area of Science:
- Computational Physics
- Machine Learning Applications
- Statistical Mechanics
Background:
- Traditional methods struggle with hard-to-sample systems.
- Machine learning offers new simulation approaches.
- Theoretical understanding of these methods is limited.
Purpose of the Study:
- To provide a theoretical analysis of global annealing (sequential tempering) with a MADE architecture.
- To understand optimal training and weights for gradient descent optimization.
- To compare global annealing with and without local Metropolis Monte Carlo steps.
Main Methods:
- Analytic study of global annealing procedure.
- Application to a shallow MADE architecture.
- Curie-Weiss model simulation.
Main Results:
- Description of optimal weights and gradient descent training.
- Comparison of global annealing with and without local Monte Carlo steps.
- Theoretical insights into optimal procedures for this system.
Conclusions:
- Establishes a theoretical basis for integrating machine learning into Monte Carlo sampling.
- Provides guidance for optimizing machine learning-assisted simulations.
- Highlights the importance of theoretical understanding for effective implementation.
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