Variational Inference Using Material Point Method

TL;DR

This paper introduces MPM-ParVI, a novel gradient-based particle sampling method leveraging the material point method to simulate deformable bodies, enabling deterministic variational inference for complex probabilistic models.

Contribution

It presents a new particle sampling approach using MPM for variational inference, combining physical simulation with probabilistic modeling.

Findings

Enables deterministic sampling for intractable densities.

Applicable to Bayesian inference and generative modeling.

Offers an easy-to-implement inference method.

Abstract

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).