A Survey of Nonlinear Filtering Methods for Data Assimilation and Recent Advances in Generative AI-Enabled Score Filters

arXiv:2611.07160v1 Announce Type: new Abstract: Many real-world applications, such as numerical weather prediction or wildfire tracking, involve modeling highly nonlinear dynamical systems that are chaotic and influenced by various sources of uncertainty. To improve model prediction accuracy and reduce such uncertainties, data assimilation (DA) combines the dynamical model with partial, noisy observations to estimate the evolution of the system's state. Doing so depends on solving the optimal filtering problem: computing the conditional distribution of a hidden state given a sequence of observations.