The forward problem is an important one in Uncertainty Quantification. It quantifies the uncertainties propagation by calculating relevant statistics. One of them is the expected value of an output’s model when the input parameters are sampled from a certain probability distribution.

This work introduces a new method to estimate the expectation of the high-fidelity model, which we term Multifidelity Dimension-Adaptive Sparse Grid Quadrature (MDASGQ). It is a prescriptive algorithm where the user defines the high-fidelity model and a set of low-fidelity models, together with a set of approximation levels used to compute the models’ estimators. The procedure explores a two-dimensional abstract space of models’ fidelities and tolerances, until a user-defined maximum refinement is reached. Then, the MDASGQ algorithm outputs an estimation of the high-fidelity model expectation, computed as in the Sparse Grid techniques.

Broadly speaking, our method combines principles from Multifidelity Monte-Carlo (MFMC) and Dimension-Adaptive Sparse Grids (DASG) techniques. Our procedure empirically proved its efficiency through multiple simulation settings of a toy problem.

Keywords: Uncertainty Quantification, Sparse Grids, Quadrature, Multifidelity Methods