On posterior consistency of data assimilation with Gaussian process priors: The 2D-Navier–Stokes equations
高斯过程先验下数据同化的后验一致性：二维Navier–Stokes方程
We consider a nonlinear Bayesian data assimilation model for the periodic two-dimensional Navier–Stokes equations with initial condition modelled by a Gaussian process prior. We show that if the system is updated with sufficiently many discrete noisy measurements of the velocity field, then the posterior distribution eventually concentrates near the ground truth solution of the time evolution equation, and in particular that the initial condition is recovered consistently by…