TY - JOUR

T1 - Adaptive Monte Carlo augmented with normalizing flows

AU - Gabrié, Marylou

AU - Rotskoff, Grant M.

AU - Vanden-Eijnden, Eric

N1 - Funding Information:
ACKNOWLEDGMENTS. G.M.R. acknowledges support from the Terman Faculty Fellowship. E.V.-E. acknowledges partial support from NSF Materials Research Science and Engineering Center Program Grant DMR-1420073, NSF Grant DMS-1522767, and a Vannevar Bush Faculty Fellowship.
Publisher Copyright:
© 2022 National Academy of Sciences. All rights reserved.

PY - 2022/3/8

Y1 - 2022/3/8

N2 - Many problems in the physical sciences,machine learning, and statistical inference necessitate sampling from a high-dimensional, multimodal probability distribution. Markov Chain Monte Carlo (MCMC) algorithms, the ubiquitous tool for this task, typically rely on random local updates to propagate configurations of a given system in a way that ensures that generated configurations will be distributed according to a target probability distribution asymptotically. In high-dimensional settings with multiple relevant metastable basins, local approaches require either immense computational effort or intricately designed importance sampling strategies to capture information about, for example, the relative populations of such basins. Here, we analyze an adaptive MCMC, which augments MCMC sampling with nonlocal transition kernels parameterized with generative models known as normalizing flows. We focus on a setting where there are no preexisting data, as is commonly the case for problems in which MCMC is used. Our method uses 1) an MCMC strategy that blends local moves obtained from any standard transition kernel with those from a generative model to accelerate the sampling and 2) the data generated thisway to adapt the generative model and improve its efficacy in the MCMC algorithm.We provide a theoretical analysis of the convergence properties of this algorithm and investigate numerically its efficiency, in particular in terms of its propensity to equilibrate fast between metastable modes whose rough location is known a priori but respective probability weight is not. We show that our algorithm can sample effectively across large free energy barriers, providing dramatic accelerations relative to traditional MCMC algorithms.

AB - Many problems in the physical sciences,machine learning, and statistical inference necessitate sampling from a high-dimensional, multimodal probability distribution. Markov Chain Monte Carlo (MCMC) algorithms, the ubiquitous tool for this task, typically rely on random local updates to propagate configurations of a given system in a way that ensures that generated configurations will be distributed according to a target probability distribution asymptotically. In high-dimensional settings with multiple relevant metastable basins, local approaches require either immense computational effort or intricately designed importance sampling strategies to capture information about, for example, the relative populations of such basins. Here, we analyze an adaptive MCMC, which augments MCMC sampling with nonlocal transition kernels parameterized with generative models known as normalizing flows. We focus on a setting where there are no preexisting data, as is commonly the case for problems in which MCMC is used. Our method uses 1) an MCMC strategy that blends local moves obtained from any standard transition kernel with those from a generative model to accelerate the sampling and 2) the data generated thisway to adapt the generative model and improve its efficacy in the MCMC algorithm.We provide a theoretical analysis of the convergence properties of this algorithm and investigate numerically its efficiency, in particular in terms of its propensity to equilibrate fast between metastable modes whose rough location is known a priori but respective probability weight is not. We show that our algorithm can sample effectively across large free energy barriers, providing dramatic accelerations relative to traditional MCMC algorithms.

KW - Free energy calculations

KW - Monte Carlo

KW - Normalizing flows

KW - Phase transitions

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U2 - 10.1073/pnas.2109420119

DO - 10.1073/pnas.2109420119

M3 - Article

C2 - 35235453

AN - SCOPUS:85125613709

SN - 0027-8424

VL - 119

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

IS - 10

M1 - e2109420119

ER -