Goal-oriented error estimation for the reduced basis method, with application to sensitivity analysis
For researchers using reduced basis methods for parametrized PDEs, this provides a more accurate error estimate, improving reliability in sensitivity analysis.
The paper proposes a new probabilistic error bound for the reduced basis method that is sharper than existing bounds, as demonstrated on multiple examples, and applies it to sensitivity analysis.
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.