Data Assimilation: The Schrödinger Perspective
Provides a foundational framework for researchers in data assimilation, stochastic processes, and optimal transport, though it is a survey rather than a novel algorithmic contribution.
This survey unifies sequential data assimilation techniques under the Schrödinger bridge problem, providing a novel perspective that connects particle-based algorithms with optimal transport and measure coupling.
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 Schrödinger's boundary value problem for stochastic processes in particular.