  Although the no-u-turn sampler (NUTS) is a widely adopted method for
performing Bayesian inference, it requires numerous posterior gradients which
can be expensive to compute in practice. Recently, there has been a significant
interest in physics-based machine learning of dynamical (or Hamiltonian)
systems and Hamiltonian neural networks (HNNs) is a noteworthy architecture.
But these types of architectures have not been applied to solve Bayesian
inference problems efficiently. We propose the use of HNNs for performing
Bayesian inference efficiently without requiring numerous posterior gradients.
We introduce latent variable outputs to HNNs (L-HNNs) for improved expressivity
and reduced integration errors. We integrate L-HNNs in NUTS and further propose
an online error monitoring scheme to prevent sampling degeneracy in regions
where L-HNNs may have little training data. We demonstrate L-HNNs in NUTS with
online error monitoring considering several complex high-dimensional posterior
densities and compare its performance to NUTS.
