# Variational Inference Using Material Point Method

arXiv: https://arxiv.org/abs/2407.20287 · HTML: https://mlsanity.com/paper/2407.20287/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 85 references that are in the map.
- First posted on arXiv 26 Jul 2024.

## Builds on (most cited first, 8 of 8)

- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [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)
- [Particle-based Energetic Variational Inference](https://mlsanity.com/paper/2004.06443/) (2020)
- [Nature-Inspired Optimization Algorithms: Challenges and Open Problems](https://mlsanity.com/paper/2003.03776/) (2020)
- [Classification via score-based generative modelling](https://mlsanity.com/paper/2207.11091/) (2022)
- [Electrostatics-based particle sampling and approximate inference](https://mlsanity.com/paper/2406.20044/) (2024)
- [Variational Inference via Smoothed Particle Hydrodynamics](https://mlsanity.com/paper/2407.09186/) (2024)

## Abstract (arXiv)

A new gradient-based particle sampling method, MPM-ParVI, based on material point method (MPM), is proposed for variational inference. MPM-ParVI simulates the deformation of a deformable body (e.g. a solid or fluid) under external effects driven by the target density; transient or steady configuration of the deformable body approximates the target density. The continuum material is modelled as an interacting particle system (IPS) using MPM, each particle carries full physical properties, interacts and evolves following conservation dynamics. This easy-to-implement ParVI method offers deterministic sampling and inference for a class of probabilistic models such as those encountered in Bayesian inference (e.g. intractable densities) and generative modelling (e.g. score-based).