  A new variational inference method, SPH-ParVI, based on smoothed particle
hydrodynamics (SPH), is proposed for sampling partially known densities (e.g.
up to a constant) or sampling using gradients. SPH-ParVI simulates the flow of
a fluid under external effects driven by the target density; transient or
steady state of the fluid approximates the target density. The continuum fluid
is modelled as an interacting particle system (IPS) via SPH, where each
particle carries smoothed properties, interacts and evolves as per the
Navier-Stokes equations. This mesh-free, Lagrangian simulation method offers
fast, flexible, scalable and deterministic sampling and inference for a class
of probabilistic models such as those encountered in Bayesian inference and
generative modelling.
