Variational Inference via Smoothed Particle Hydrodynamics

TL;DR

The paper introduces SPH-ParVI, a novel variational inference method that uses smoothed particle hydrodynamics to efficiently sample from complex probability densities by simulating fluid flow.

Contribution

It presents a new mesh-free, Lagrangian particle-based approach for variational inference leveraging fluid dynamics principles, enhancing scalability and flexibility.

Findings

Provides a scalable particle-based inference algorithm.

Achieves fast and deterministic sampling.

Applicable to Bayesian and generative models.

Abstract

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.