Multilevel Markov Chain Monte Carlo for Bayesian inverse problems for Navier Stokes equation with Lagrangian Observations
<|reference_start|>Multilevel Markov Chain Monte Carlo for Bayesian inverse problems for Navier Stokes equation with Lagrangian Observations: In this paper, we extend our work to the Bayesian inverse problems for inferring unknown forcing and initial condition of the forward Navier-Stokes equation coupled with tracer equation with noisy Lagrangian observation on the positions of the tracers. We consider the Navier-Stokes equations in the two dimensional periodic torus with a tracer equation which is a simple ordinary differential equation. We developed rigorously the theory for the case of the uniform prior where the forcing and the initial condition depend linearly on a countable set of random variables which are uniformly distributed in a compact interval. Numerical experiment using the MLMCMC method produces approximations for posterior expectation of quantities of interest which are in agreement with the theoretical optimal convergence rate established.<|reference_end|>
@article{yang2024multilevel,
    title={Multilevel Markov Chain Monte Carlo for Bayesian inverse problems for
  Navier Stokes equation with Lagrangian Observations},
    author={Juntao Yang},
    journal={arXiv preprint arXiv:2403.12501},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.12501},
    primaryClass={math.NA cs.NA}
}