Goal-oriented error estimation for the reduced basis method, with application to sensitivity analysis

TL;DR

This paper introduces a new probabilistic error bound for the reduced basis method, improving accuracy and efficiency, with applications demonstrated in sensitivity analysis of parametrized PDEs.

Contribution

A novel probabilistic error bound for the reduced basis method that is sharper and more computationally efficient than existing bounds, with practical applications in sensitivity analysis.

Findings

The new error bound is sharper than existing bounds.

The error bound is efficiently and explicitly computable.

Applications to sensitivity analysis demonstrate practical benefits.

Abstract

The reduced basis method is a powerful model reduction technique designed to speed up the computation of multiple numerical solutions of parametrized partial differential equations. We consider a quantity of interest, which is a linear functional of the PDE solution. A new probabilistic error bound for the reduced model is proposed. It is efficiently and explicitly computable, and we show on different examples that this error bound is sharper than existing ones. We include application of our work to sensitivity analysis studies.