CFC 2023
Date:
This work has been motivated by data assimilation in blood flow models. In many realistic applications, the knowledge of the model parameters as well as the boundary conditions is not perfect. We focus here on the estimation of the input parameters from observations of the output solution. The resulting estimate is then exploited to perform uncertainty quantification tasks. However, there are two major difficulties when trying to solve parameter estimation problems. First, some parameters may not be identifiable. For instance, if only partial noisy measurements of the solution are available, several different parameter values may be associated with the same observation. Second, if the parameters depend nonlinearly on the solution, the parameter estimation problem results in a nonlinear non-convex optimization problem that can be difficult to solve. For these reasons, we employ a sequential Markov Chain Monte Carlo (MCMC) method using the Metropolis-Hasting algorithm to estimate the parameters. This bayesian approach consists in sampling the posterior probability distribution of the parameters and allows to identify eventual correlations between the parameter values. However, updating this sampling is computationally expensive since the solution must be evaluated repeatedly for each queried parameter. For this reason, we developed a low-rank solver to significantly reduce the time and storage requirements associated with the MCMC procedure. The performance of the resulting method is demonstrated on three different applications.