Data assimilation: A dynamic homotopy-based coupling approach

TL;DR

This paper introduces a novel homotopy-based method for data assimilation that extends ensemble Kalman filters to solve Schr"odinger bridge problems, enabling more effective Bayesian inference with complex distributions.

Contribution

It extends homotopy approaches to include stochastic diffusion processes and adapts ensemble Kalman filters to Schr"odinger bridge problems for sequential data assimilation.

Findings

Provides a computationally feasible approximation to the Schr"odinger bridge problem.

Extends ensemble Kalman filter methodology to new stochastic diffusion contexts.

Demonstrates improved data assimilation performance in complex Bayesian inference scenarios.

Abstract

Homotopy approaches to Bayesian inference have found widespread use especially if the Kullback-Leibler divergence between the prior and the posterior distribution is large. Here we extend one of these homotopy approach to include an underlying stochastic diffusion process. The underlying mathematical problem is closely related to the Schr\"odinger bridge problem for given marginal distributions. We demonstrate that the proposed homotopy approach provides a computationally tractable approximation to the underlying bridge problem. In particular, our implementation builds upon the widely used ensemble Kalman filter methodology and extends it to Schr\"odinger bridge problems within the context of sequential data assimilation.