# Electrostatics-based particle sampling and approximate inference

arXiv: https://arxiv.org/abs/2406.20044 · HTML: https://mlsanity.com/paper/2406.20044/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 56 references that are in the map.
- First posted on arXiv 28 Jun 2024.

## Builds on (most cited first, 13 of 13)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Maximum Mean Discrepancy Gradient Flow](https://mlsanity.com/paper/1906.04370/) (2019)
- [A Unified Particle-Optimization Framework for Scalable Bayesian Sampling](https://mlsanity.com/paper/1805.11659/) (2018)
- [Stein Variational Gradient Descent With Matrix-Valued Kernels](https://mlsanity.com/paper/1910.12794/) (2019)
- [Particle-based Energetic Variational Inference](https://mlsanity.com/paper/2004.06443/) (2020)
- [Variational Particle Approximations](https://mlsanity.com/paper/1402.5715/) (2014)
- [Particle-based Online Bayesian Sampling](https://mlsanity.com/paper/2302.14796/) (2023)
- [Approximating Bayes in the 21st Century](https://mlsanity.com/paper/2112.10342/) (2021)

## Built on by (most cited first, 2 of 2)

- [Variational Inference via Smoothed Particle Hydrodynamics](https://mlsanity.com/paper/2407.09186/) (2024)
- [Variational Inference Using Material Point Method](https://mlsanity.com/paper/2407.20287/) (2024)

## Abstract (arXiv)

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.