Neural Surrogate HMC: On Using Neural Likelihoods for Hamiltonian Monte Carlo in Simulation-Based Inference
This work addresses computational bottlenecks in simulation-based inference for researchers in fields like astrophysics, though it is incremental as it builds on existing methods.
The paper tackles the problem of Bayesian inference when likelihood computations are infeasible by combining neural likelihood estimation with Hamiltonian Monte Carlo, enabling efficient inference in simulation-based scenarios, as demonstrated in a heliospheric transport model.
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.