A Low-Rank Solver for Parameter Estimation and Uncertainty Quantification in Time-Dependent Systems of Partial Differential Equations

In this work we propose a low-rank solver in view of performing parameter estimation and uncertainty quantification in systems of partial differential equations. The solution approximation is sought in a space-parameter separated form. The discretisation in the parameter direction is made evolve in time through a Markov Chain Monte Carlo method. The resulting method is a Bayesian sequential estimation of the parameters. The computational burden is mitigated by the introduction of an efficient interpolator, based on a reduced basis built by exploiting the low-rank solves. The method is tested on four different applications.