发表机构
Westlake University; Zhejiang University（西湖大学; 浙江大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出信念流滤波器（BFF），通过测试时梯度下降更新流匹配模型权重以跟踪后验演化，绕过粒子表示和高斯假设的限制，在多个物理系统基准上取得最优性能。
AI 中文摘要
贝叶斯滤波为不确定性下的在线状态估计提供了 principled 框架，然而将其应用于具有高维状态和复杂后验分布的系统仍具挑战性。最近的生成模型，如流匹配，已在贝叶斯滤波中显示出潜力。然而，它们仍依赖基于粒子的后验表示，这丢失了完整分布的丰富信息，或者处理与贝叶斯滤波递归结构相冲突的轨迹级逆问题。为解决此问题，我们提出一种新视角，即将演化分布直接编码到流匹配模型权重中，即信念流滤波器（Belief Flow Filter, BFF）。这是一种生成式滤波框架，在测试时通过梯度下降更新模型权重以跟踪后验演化。由此，BFF 绕过了粒子表示的可扩展性问题或传统滤波器中高斯假设的灵活性限制。我们从理论上证明 BFF 的设计在结构上与贝叶斯滤波一致，其训练目标针对递归滤波算子。BFF 在 5 个不同的物理系统上进行了实证验证，包括具有混沌动力学和高度稀疏、非线性观测的系统。结果表明，在三个标准 1D 和 2D PDE 基准中，BFF 在 9 个指标-基准单元中的 8 个上取得最佳分数，并且在极端单移动传感器设置和基于真实世界的托卡马克等离子体估计任务上同样领先，展示了其在高维概率空间中准确近似贝叶斯滤波算子的潜力。
英文摘要
Bayesian filtering provides a principled framework for online state estimation under uncertainty, yet its application to systems with high-dimensional states and complicated posterior distributions remains challenging. Recent generative models, such as flow matching, have shown potential in Bayesian filtering. However, they still rely on particle-based representations of the posterior, which lose the rich information of the full distribution, or tackle a trajectory-level inverse problem that conflicts with the recursive structure of Bayesian filtering. To address this, we propose a new perspective of directly encoding the evolving distribution into flow matching model weights, namely, the Belief Flow Filter (BFF). It is a generative filtering framework that updates model weights via gradient descent at test time to track the posterior evolution. Thereby, BFF bypasses the scalability issue of particle representations or the flexibility limitation of Gaussian assumptions in conventional filters. We theoretically justify that the BFF design is structurally aligned with Bayesian filtering, and its training objective targets the recursive filtering operator. BFF is empirically verified across 5 different physical systems, including ones with chaotic dynamics and highly sparse, non-linear observations. The results show that BFF attains the best score in 8 of 9 metric-benchmark cells across the three standard 1D and 2D PDE benchmarks, and similarly leads on the extreme single-moving-sensor setting and on a real-world-grounded tokamak plasma estimation task, demonstrating its potential to accurately approximate the Bayesian filtering operator in high-dimensional probability space.
