Generative models for simulation based filtering: Formulations and Empirical Comparisons

2026-09-14

AI Summary

本文提出了一种统一的生成模型方法来解决非线性滤波问题，并通过数值比较评估了基于不同传输学习方式的新滤波器，对比了其准确性、计算时间和对集合大小及状态维度的敏感性。

Abstract

This letter presents a unified formulation and a controlled numerical comparison of generative-model approaches to the nonlinear filtering problem. Under this formulation the analysis step is realized by a transport of the forecast distribution to the posterior, the approaches differing only in how that transport is selected and learned. We derive three new filters, based on stochastic interpolants, their deterministic flow-matching limit, and Schrödinger bridges realized through forward--backward SDEs. We develop a two-stage tuning procedure that separates the training of the generative model from its online refinement. The resulting methods are compared against the optimal transport filter (OTF), the Knothe--Rosenblatt filter (KRF), the sequential importance resampling (SIR) particle filter and the ensemble Kalman filter (EnKF), in terms of accuracy, computational time, and sensitivity to ensemble size and state dimension. The results indicate that every generative filter resolves multimodal posteriors that the EnKF and SIR do not, that no single generative framework dominates, the preferred method being set by the available online budget and ensemble size, and that the filters differ in the regularity of the particle trajectories they produce.

Problem

• nonlinear filtering
• generative models
• forecast distribution
• posterior
• transport

Innovation

• generative model
• nonlinear filtering
• stochastic interpolants
• Schrödinger bridges
• two-stage tuning