Accelerating Markov Chain Monte Carlo sampling with diffusion models

Journal Article · 13 December 2023 · Computer Physics Communications

DOI: https://doi.org/10.1016/j.cpc.2023.109059 · OSTI ID:2281802

Hunt-Smith, Nicholas T.  ^[1]; Melnitchouk, Wally ^[2]; Ringer, Felix ^[3]; Sato, Nobuo ^[2]; Thomas, Anthony W. ^[1]; White, Martin J. ^[1]

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1. Univ. of Adelaide, SA (Australia). CSSM and ARC Centre of Excellence for Dark Matter Particle Physics
2. Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
3. Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Old Dominion Univ., Norfolk, VA (United States)

Global fits of physics models require efficient methods for exploring high-dimensional and/or multimodal posterior functions. We introduce a novel method for accelerating Markov Chain Monte Carlo (MCMC) sampling by pairing a Metropolis-Hastings algorithm with a diffusion model that can draw global samples with the aim of approximating the posterior. We briefly review diffusion models in the context of image synthesis before providing a streamlined diffusion model tailored towards low-dimensional data arrays. We then present our adapted Metropolis-Hastings algorithm which combines local proposals with global proposals taken from a diffusion model that is regularly trained on the samples produced during the MCMC run. Our approach leads to a significant reduction in the number of likelihood evaluations required to obtain an accurate representation of the Bayesian posterior across several analytic functions, as well as for a physical example based on a global fit of parton distribution functions. Our method is extensible to other MCMC techniques, and we briefly compare our method to similar approaches based on normalising flows. A code implementation can be found at https://github.com/NickHunt-Smith/MCMC-diffusion.

• Research Organization: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Nuclear Physics (NP); ARC Centre of Excellence
• Grant/Contract Number: AC05-06OR23177; CE200100008
• OSTI ID: 2281802
• Report Number(s): JLAB-THY-23-3900; DOE/OR/23177-7034; CE200100008; TRN: US2408377
• Journal Information: Computer Physics Communications, Vol. 296; ISSN 0010-4655
• Publisher: ElsevierCopyright Statement
• Country of Publication: United States
• Language: English