2024/11/20 by Zhao Ding, Chenguang Duan, Ding, Zhao +9 · 2 citations
Computer Science · Environmental Science · Mathematics · #Climate variability and models #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #cs.NA #math.NA #math.OC #stat.ML
paper · pdf · doi:10.48550/arxiv.2411.13443
published as IEEE Transactions on Information Theory, 2026
openalex publication_date 2024/11/20 · openalex created_date 2024/11/24 · arxiv created 2026/04/04 · openalex updated_date 2026/07/28 · arxiv updated 2026/08/03
This paper introduces score-based sequential Langevin sampling (SSLS), a novel approach to nonlinear data assimilation within a recursive Bayesian filtering framework. The proposed method decomposes the assimilation process into alternating prediction and update steps, using dynamic models for state prediction and incorporating observational data via score-based Langevin Monte Carlo during the updates. To overcome inherent challenges in highly non-log-concave posterior sampling, we integrate an annealing strategy into the update mechanism. Theoretically, we establish convergence guarantees for SSLS in total variation (TV) distance, yielding concrete insights into the algorithm's error behavior with respect to key hyperparameters. Crucially, our derived error bounds demonstrate the asymptotic stability of SSLS, guaranteeing that local posterior sampling errors do not accumulate indefinitely over time. Extensive numerical experiments across challenging scenarios, including high-dimensional systems, strong nonlinearity, and sparse observations, highlight the robust performance of the proposed method. Furthermore, SSLS effectively quantifies the uncertainty associated with state estimates, rendering it particularly valuable for reliable error calibration.