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This research demonstrates a powerful synergy between neural likelihood estimation and Hamiltonian Monte Carlo, enabling efficient Bayesian inference in scenarios where direct likelihood computation is impossible. By using machine learning to amortize computations and provide necessary gradients, the method effectively handles noisy simulations from numerical instabilities while modeling complex astrophysical phenomena like galactic cosmic ray transport.
Neural Surrogate HMC: On Using Neural Likelihoods for Hamiltonian Monte Carlo in Simulation-Based Inference
arXiv:2407.20432v3 Announce Type: replace Abstract: Bayesian inference methods such as Markov Chain Monte Carlo (MCMC) typically require repeated computations of the likelihood function, but in some scenarios this is infeasible and alternative methods are needed. Simulation-based inference (SBI) methods address this problem by using machine learning to amortize computations. In this work, we highlight a particular synergy between the SBI method of neural likelihood estimation and the classic MCMC method of Hamiltonian Monte Carlo. We show that approximating the likelihood function with a neural network model can provide three distinct advantages: (1) amortizing the computations for MCMC; (2) providing gradients for Hamiltonian Monte Carlo, and (3) smoothing over noisy simulations resulting from numerical instabilities. We provide practical guidelines for defining a prior, sampling a training set, and evaluating convergence. The method is demonstrated in an application modeling the heliospheric transport of galactic cosmic rays, where it enables efficient inference of latent parameters in the Parker equation.
Abstract:Bayesian inference methods such as Markov Chain Monte Carlo (MCMC) typically require repeated computations of the likelihood function, but in some scenarios this is infeasible and alternative methods are needed. Simulation-based inference (SBI) methods address this problem by using machine learning to amortize computations. In this work, we highlight a particular synergy between the SBI method of neural likelihood estimation and the classic MCMC method of Hamiltonian Monte Carlo. We show that approximating the likelihood function with a neural network model can provide three distinct advantages: (1) amortizing the computations for MCMC; (2) providing gradients for Hamiltonian Monte Carlo, and (3) smoothing over noisy simulations resulting from numerical instabilities. We provide practical guidelines for defining a prior, sampling a training set, and evaluating convergence. The method is demonstrated in an application modeling the heliospheric transport of galactic cosmic rays, where it enables efficient inference of latent parameters in the Parker equation.
22 pages, 17 figures. Accepted for publication in the Journal of Geophysical Research: Machine Learning and Computation. Published 2026 American Geophysical Union. Further reproduction or electronic distribution is not permitted
Machine Learning (cs.LG); High Energy Astrophysical Phenomena (astro-ph.HE)
arXiv:2407.20432 [cs.LG]
(or arXiv:2407.20432v3 [cs.LG] for this version)
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