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).

翻译：本文提出了一种基于物质点法（MPM）的新型梯度粒子采样方法MPM-ParVI，用于变分推断。MPM-ParVI模拟可变形体（如固体或流体）在目标密度驱动的外部作用下的形变过程；可变形体的瞬态或稳态构型即近似于目标密度。该方法通过MPM将连续介质材料建模为相互作用的粒子系统（IPS），每个粒子携带完整的物理属性，并遵循守恒动力学进行相互作用与演化。这种易于实现的ParVI方法为一类概率模型（如贝叶斯推断中遇到的难解密度模型与生成建模中的基于分数的模型等）提供了确定性采样与推断能力。