Parametric PDE solvers for parameter estimation and Uncertainty Quantification
Résumé
A parametric PDE solver is presented. After a classical semi-discretisation in time, the weak formulation of the problem is considered both in space and parameters. A separation of variable principle is applied to give a parsimonious representation of the parametric solution. The non-linear problem arising is solved by means of a fixed-point and the TT-GMRES method. Such a parametric solver is applied in the context of Bayesian parameter estimation and enables sequential estimation and UQ (on the posterior) even for large systems. Several encouraging results are presented.