论文标题
数据同化：一种基于动态同质的耦合方法
Data assimilation: A dynamic homotopy-based coupling approach
论文作者
论文摘要
贝叶斯推论的同型方法已经发现了广泛的使用，特别是如果先前和后验分布之间的kullback-leibler差异很大。在这里，我们扩展了这些同质方法之一，以包括潜在的随机扩散过程。潜在的数学问题与给定边缘分布的Schrödinger桥问题密切相关。我们证明了所提出的同型方法为基础桥问题提供了可计算的近似值。特别是，我们的实现建立在广泛使用的集合Kalman滤波器方法基础上，并将其扩展到顺序数据同化的背景下的Schrödinger桥问题。
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 Schrödinger 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 Schrödinger bridge problems within the context of sequential data assimilation.
