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Adaptive Monte Carlo augmented with normalizing flows.

Marylou Gabrié1,2, Grant M Rotskoff3, Eric Vanden-Eijnden4

  • 1Center for Computational Mathematics, Flatiron Institute, New York, NY 10010.

Proceedings of the National Academy of Sciences of the United States of America
|March 2, 2022
PubMed
Summary
This summary is machine-generated.

Generative models accelerate Monte Carlo sampling for complex probability distributions. This machine learning approach overcomes computational challenges in physical sciences and statistics.

Keywords:
Monte Carlofree energy calculationsnormalizing flowsphase transitions

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Area of Science:

  • Computational physics and applied mathematics.
  • Bayesian statistics and machine learning.

Background:

  • Monte Carlo methods are essential for sampling probability distributions but can be computationally intensive due to slow "mixing".
  • Designing efficient sampling schemes often requires system-specific, hand-tuned algorithms.
  • Generative models present a promising alternative for accelerating these sampling processes.

Purpose of the Study:

  • To formalize a novel approach combining Monte Carlo methods with normalizing flows.
  • To demonstrate the acceleration of sampling using generative models.
  • To show the effectiveness of this method with limited data and a physically inspired algorithm.

Main Methods:

  • Integration of normalizing flows within the Monte Carlo framework.
  • Development of a physically inspired algorithm to guide the generative model.
  • Utilizing limited prior data to train the generative model.

Main Results:

  • Substantial acceleration of Monte Carlo sampling was achieved.
  • The proposed method demonstrates efficiency even with limited training data.
  • The physically inspired algorithm enhances the performance of generative models for sampling.

Conclusions:

  • Normalizing flows augmented with Monte Carlo methods offer a powerful alternative to traditional sampling techniques.
  • This approach significantly reduces computational costs associated with complex probability distributions.
  • The combination of machine learning and physics-based insights provides a scalable solution for scientific sampling challenges.