Repository: Freie Universit├Ąt Berlin, Math Department

On posterior consistency of data assimilation with Gaussian process priors: the 2D Navier-Stokes equations

Nickl, Richard and Titi, Edriss (2023) On posterior consistency of data assimilation with Gaussian process priors: the 2D Navier-Stokes equations. ArXive . (Unpublished)

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Official URL: https:\\arxiv:2307.08136v1

Abstract

We consider a non-linear 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 distri- bution eventually concentrates near the ground truth solution of the time evolu- tion equation, and in particular that the initial condition is recovered consistently by the posterior mean vector field. We further show that the convergence rate can in general not be faster than inverse logarithmic in sample size, but describe specific conditions on the initial conditions when faster rates are possible. In the proofs we provide an explicit quantitative estimate for backward uniqueness of solutions of the two-dimensional Navier-Stokes equations.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:3022
Deposited By: Monika Drueck
Deposited On:17 Aug 2023 11:15
Last Modified:17 Aug 2023 11:15

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