arXiv Machine Learning
Sep 22

Bayesian Filtering in Physical Systems via Test-time Trained Flow Matching

The paper introduces the Belief Flow Filter (BFF), a generative filtering framework that encodes the evolving posterior distribution directly into flow matching model weights and updates them via test‑time gradient descent. By avoiding particle representations and Gaussian assumptions, BFF aligns structurally with Bayesian filtering and targets the recursive filtering operator. Empirical results on five physical systems—including chaotic dynamics, sparse observations, and a tokamak plasma estimation task—show that BFF outperforms existing methods in most benchmark metrics.

By Ruiqi Feng, Chongyi Wang, Tao Zhang, Tailin Wu