A new particle-based sampling and approximate inference method, based on electrostatics and Newton mechanics principles, is introduced with theoretical ground, algorithm design and experimental validation. This method simulates an interacting particle system (IPS) where particles, i.e. the freely-moving negative charges and spatially-fixed positive charges with magnitudes proportional to the target distribution, interact with each other via attraction and repulsion induced by the resulting electric fields described by Poisson's equation. The IPS evolves towards a steady-state where the distribution of negative charges conforms to the target distribution. This physics-inspired method offers deterministic, gradient-free sampling and inference, achieving comparable performance as other particle-based and MCMC methods in benchmark tasks of inferring complex densities, Bayesian logistic regression and dynamical system identification. A discrete-time, discrete-space algorithmic design, readily extendable to continuous time and space, is provided for usage in more general inference problems occurring in probabilistic machine learning scenarios such as Bayesian inference, generative modelling, and beyond.

基于粒子的采样和近似推断方法，基于静电学和牛顿力学原理，提出了一种新的方法，通过模拟相互作用的粒子系统来实现确定性、无梯度的采样和推断，可应用于概率机器学习中的贝叶斯推断、生成模型等问题。

基于静电的粒子采样与近似推断