Variational Inference via Smoothed Particle Hydrodynamics

TL;DR

SPH-ParVI introduces a physics-inspired variational inference framework that uses a smoothed-particle-hydrodynamics interacting particle system to sample from densities known only up to a constant or from gradient information. It leverages two designs—external pressure for the target density and external force for its gradient—within the Navier–Stokes SPH dynamics to steer particles toward the target distribution in a mesh-free, deterministic, and scalable manner. The method formalizes sampling as a transient or equilibrated fluid configuration and discusses practical considerations (viscosity, surface tension, regularisation, adaptivity, time stepping) and tradeoffs (accuracy vs. efficiency), while outlining future work on validation, convergence, and extensions. Overall, SPH-ParVI provides a novel bridge between SPH physics and probabilistic inference, enabling efficient sampling for complex, high-dimensional densities and partially known targets.

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.

Figures (2)

• Figure 1: Illustration of the smoothing kernel (figures from nasreldeen2017sph).
• Figure 2: Smoothing kernels and gradients.