Nonlinear Assimilation via Score-based Sequential Langevin Sampling
For practitioners in fields requiring nonlinear data assimilation (e.g., geophysics, climate science), SSLS provides a theoretically grounded method that handles challenging scenarios while quantifying uncertainty, though it is an incremental improvement over existing score-based methods.
This paper introduces score-based sequential Langevin sampling (SSLS) for nonlinear data assimilation, achieving robust performance in high-dimensional, strongly nonlinear, and sparse observation settings with theoretical convergence guarantees and asymptotic stability.
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.