A low-rank solver for parameter estimation and uncertainty quantification in linear 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.

Recommended citation: S. Riffaud, M. A. Fernández, D. Lombardi, "A low-rank solver for parameter estimation and uncertainty quantification in time-dependent systems of Partial Differential Equations", Journal of Scientific Computing 99 (2024), no 2, p. 34.
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