Data Assimilation: The Schr\"odinger Perspective

TL;DR

This paper surveys sequential data assimilation methods, emphasizing probabilistic particle algorithms, and introduces a unifying framework based on measure coupling and Schr"odinger's boundary value problem for stochastic processes.

Contribution

It provides a comprehensive overview of recent developments in probabilistic data assimilation and introduces a novel unifying framework using measure coupling and Schr"odinger's problem.

Findings

Review of discrete and continuous-time data assimilation techniques

Introduction of a unifying measure coupling framework

Connection of data assimilation with Schr"odinger's boundary value problem

Abstract

Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using probabilistic particle-based algorithms. In addition to surveying recent developments for discrete- and continuous-time data assimilation, both in terms of mathematical foundations and algorithmic implementations, we also provide a unifying framework from the perspective of coupling of measures, and Schr\"odinger's boundary value problem for stochastic processes in particular.