Generative Model Proposal based Particle Filtering for Data Assimilation

Data assimilation aims to infer the latent state of a dynamical system from sequential, noisy observations. While classical methods like the Kalman Filter are efficient, they rely on restrictive linear-Gaussian assumptions. Particle Filters (PFs) can handle non-linear and non-Gaussian systems in theory, but they suffer from weight degeneracy in high dimensions, where most particles receive negligible weight. Recent generative approaches attempt to learn state transitions but often fail to perform a principled Bayesian update, leading to error accumulation over long horizons. This paper introduces the Flow Proposal Particle Filter (FPPF), which learns a proposal distribution using conditional flow matching to approximate the variance-minimizing optimal proposal, while retaining a valid Bayesian update step.

FPPF addresses the degeneracy problem by conditioning the proposal on incoming observations, effectively steering particles toward high-likelihood regions before reweighting. Because the learned proposal allows for tractable likelihood evaluation via the instantaneous change-of-variables formula, FPPF can compute accurate importance weights. To scale to high-dimensional systems, the authors introduce L-FPPF, a localized variant that uses a patch-based velocity network to factorize the proposal density, allowing for localized weight computation and resampling. Experiments on chaotic systems—including Lorenz-63, Lorenz-96, and the Kuramoto-Sivashinsky equation—demonstrate that FPPF consistently outperforms classical statistical baselines and autoregressive generative models in state estimation accuracy and probabilistic calibration. L-FPPF successfully scales to state dimensions as high as 1000, where global particle filters typically collapse.

This work bridges the gap between flexible, machine-learning-based generative models and the rigorous framework of sequential Monte Carlo. By learning an observation-informed proposal, FPPF provides a robust way to perform data assimilation in complex, non-linear environments without sacrificing the probabilistic integrity of the Bayesian update. The localized variant, L-FPPF, is particularly significant for high-dimensional scientific applications, such as weather forecasting or climate modeling, where global filters are computationally infeasible or prone to catastrophic failure.