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(Unpublished)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 |
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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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