Nonlinear Assimilation via Score-based Sequential Langevin Sampling

TL;DR

This paper presents SSLS, a new nonlinear data assimilation method using score-based Langevin sampling with convergence guarantees and robust performance in high-dimensional, nonlinear, and sparse observation scenarios.

Contribution

Introduces score-based sequential Langevin sampling (SSLS), a novel nonlinear data assimilation method with theoretical convergence guarantees and stability in complex settings.

Findings

Demonstrates convergence guarantees in total variation distance.

Shows robustness in high-dimensional, nonlinear, and sparse observation scenarios.

Effectively quantifies uncertainty in state estimates.

Abstract

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.