NeuralHMC: Accelerated Hamiltonian Monte Carlo with a Neural Network Surrogate Likelihood

Bayesian Inference with Markov Chain Monte Carlo requires the ability to efficiently compute the likelihood function. In some scientific applications, the likelihood can only be computed by a numerical PDE solver, which can be prohibitively expensive. We demonstrate that some such problems can be made tractable by amortizing the computation with a surrogate likelihood function implemented by a neural network. This can have the added benefits of reducing noise in the likelihood evaluations and providing fast gradient calculations. We demonstrate these advantages in a model of heliospheric transport of galactic cosmic rays, where our approach enables us to estimate the posterior of five latent parameters of the Parker equation.