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.

翻译：本文提出了一种新的变分推断方法SPH-ParVI，该方法基于平滑粒子流体动力学（SPH），适用于对部分已知密度（例如已知到常数倍）或可利用梯度进行采样的问题。SPH-ParVI通过模拟目标密度驱动下受外部效应影响的流体流动，使流体的瞬态或稳态分布逼近目标密度。该模型通过SPH将连续流体建模为相互作用粒子系统（IPS），其中每个粒子携带平滑化属性，并根据纳维-斯托克斯方程进行相互作用与演化。这种无网格的拉格朗日模拟方法为一类概率模型（如贝叶斯推断和生成建模中常见的模型）提供了快速、灵活、可扩展且确定性的采样与推断框架。