Population-Aware Physics-Informed Neural Particle Flow for Bayesian Update

2026-06-09

AI Summary

Standard physics-informed neural particle flow (PINPF) treats particles independently during Bayesian updating, neglecting collective structural information and thereby limiting posterior approximation accuracy. This work proposes a group-aware PINPF framework that leverages permutation-invariant Deep Sets to encode the state or physical features of the entire particle ensemble into a group context, which guides individual particle transport. For the first time, two group encoding mechanisms—state-level and feature-level—are introduced to incorporate collective physical information into the unsupervised Bayesian particle evolution process, enhancing the model’s capacity to capture the geometric structure of the posterior distribution. Experiments on range measurement and nonlinear time-difference-of-arrival tasks demonstrate that the proposed approach significantly outperforms the original PINPF, with feature-level encoding achieving the best performance, thereby validating the efficacy of leveraging group physical features.

Abstract

Physics-informed neural particle flow (PINPF) learns a deterministic transport field that moves particles from a prior distribution toward a Bayesian posterior while enforcing the governing probability-evolution equation. However, the standard PINPF velocity model processes particles independently and therefore does not explicitly condition its transport decisions on the empirical particle population. This paper introduces population-aware PINPF (PA-PINPF), which augments each particle update with a permutation-invariant Deep Sets representation of the full particle set. We investigate two population encoders. PA-PINPF-State summarizes the particle states, whereas PA-PINPF-Feature summarizes the complete local physics-informed feature vectors, including particle position, pseudo-time, measurement information, likelihood values, and score information. The latter allows the population context to represent not only particle-cloud geometry, but also the population-level Bayesian transport geometry. The methods retain the original unsupervised physics-informed residual objective and require no ground-truth posterior samples during training. Experiments on range-measurement tasks and nonlinear time-difference-of-arrival posterior transport demonstrate that both population-aware variants improve over particle-wise PINPF, while feature-population encoding provides the strongest performance. These results show that population-level physics features provide useful global information for learned Bayesian particle transport.

Problem

• population-aware
• physics-informed neural particle flow
• Bayesian update
• particle transport
• Deep Sets

Innovation

• population-aware
• physics-informed neural particle flow
• Deep Sets
• Bayesian inference
• permutation-invariant encoding