Ensemble transport smoothing. Part II: Nonlinear updates

TL;DR

This paper introduces nonlinear backward ensemble transport smoothers for Bayesian state estimation, demonstrating improved accuracy over traditional linear methods in nonlinear and chaotic systems.

Contribution

It extends transport-based ensemble smoothing to nonlinear updates, including parameterization and regularization of transport maps, and evaluates performance on complex dynamical systems.

Findings

Nonlinear smoothers outperform linear ones in chaotic systems.

Transport smoothers achieve lower estimation error with similar computational effort.

Demonstrated effectiveness on non-Gaussian, nonlinear dynamical models.

Abstract

Smoothing is a specialized form of Bayesian inference for state-space models that characterizes the posterior distribution of a collection of states given an associated sequence of observations. Ramgraber et al. (2023) proposes a general framework for transport-based ensemble smoothing, which includes linear Kalman-type smoothers as special cases. Here, we build on this foundation to realize and demonstrate nonlinear backward ensemble transport smoothers. We discuss parameterization and regularization of the associated transport maps, and then examine the performance of these smoothers for nonlinear and chaotic dynamical systems that exhibit non-Gaussian behavior. In these settings, our nonlinear transport smoothers yield lower estimation error than conventional linear smoothers and state-of-the-art iterative ensemble Kalman smoothers, for comparable numbers of model evaluations.