Pareto Framework for Bayesian-Validated Computer-Simulation Surrogates

摘要

In this project we have developed a two-stage off-line/on-line blackbox reduced-basis output bound method for the prediction of outputs (quantities of interest) of elliptic partial differential equations with affine parameter dependence. The computational complexity of the on-line stage of the procedure scales only with the dimension of the reduced-basis space and the parametric complexity of the partial differential operator. The method is both efficient and certain: thanks to rigorous a posteriori error bounds, we may (safely) retain only the minimal number of modes necessary to achieve the prescribed accuracy in the output of interest. The technique is particularly appropriate for applications such as design and optimization, in which repeated and rapid evaluation of the output is required.