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.
arXiv:2607. 01012v1 Announce Type: new Abstract: Data assimilation models state dynamics conditioned on sequential observations, and has wide-ranging scientific applications.
arXiv:2606. 26497v1 Announce Type: new Abstract: Bayesian filtering of partially and noisily observed dynamical systems seeks to infer the evolving conditional distribution of the state of a dynamical system, given observations, in an online fashion.
arXiv:2508. 13313v4 Announce Type: replace-cross Abstract: Data assimilation (DA) estimates a dynamical system's state from noisy observations.
arXiv:2609.16317v1 Announce Type: new Abstract: This letter presents a unified formulation and a controlled numerical comparison of generative-model approaches to the nonlinear filtering problem. Und...
arXiv:2607. 12095v1 Announce Type: cross Abstract: Sensor-rich data-driven applications increasingly use Bayesian approaches to infer latent states of dynamic systems from noisy sensor measurements and physical models.
arXiv:2604.07169v3 Announce Type: replace-cross Abstract: Bayesian filtering and smoothing are central to data assimilation in nonlinear dynamical systems. Recent advances in deep generative models p...
The paper introduces FREESIA, a training‑free, covariance‑aware posterior transport method for data assimilation that embeds forecast cross‑covariance into a flow‑based transport to recover unobserved states while preserving non‑Gaussian posterior structure. It combines an observation‑adaptive proposal with posterior correction, providing an asymptotically exact approximation of nonlinear posteriors and a Wasserstein error bound. Experiments on Double‑Well, Lorenz‑96, and Kolmogorov flow demonstrate that FREESIA captures complex posterior structures and achieves up to a 56% reduction in RMSE compared to the best baseline in sparse, nonlinear, non‑injective observation scenarios.
arXiv:2606. 10959v1 Announce Type: new 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.
arXiv:2607. 20521v1 Announce Type: new Abstract: The state of a dynamic system evolves over time, switching among several latent modes that govern its observable behavior.
arXiv:2606. 11140v1 Announce Type: cross Abstract: Data assimilation (DA) in subsurface flow entails calibrating model parameters to match observed data, typically at wells, while preserving geological realism.
arXiv:2606. 01468v1 Announce Type: cross Abstract: Due to their explicit priors and ability to model uncertainty, Bayesian methods have played a major role in dynamical latent variable modeling of single-cell neural recordings.
arXiv:2605. 15407v3 Announce Type: replace-cross Abstract: We consider amortized Bayesian inference for nonlinear inverse problems using only samples from the joint distribution of parameters and observations, including problems with unknown functions in a Banach space.