Neural Surrogate HMC: On Using Neural Likelihoods for Hamiltonian Monte Carlo in Simulation-Based Inference

TL;DR

This paper introduces Neural Surrogate HMC, a method combining neural likelihood estimation with Hamiltonian Monte Carlo to improve simulation-based Bayesian inference by amortizing computations, providing gradients, and smoothing noisy data.

Contribution

It presents a novel approach that integrates neural likelihoods with HMC, enhancing efficiency and stability in SBI, especially for complex physical models.

Findings

Enables efficient inference of cosmic ray transport parameters.

Provides practical guidelines for implementation and convergence.

Demonstrates effectiveness in modeling heliospheric transport.

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.