Speaker
Description
High-fidelity computational models of complex flows provide accurate predictions, but their significant computational cost often makes them impractical for applications requiring repeated evaluations, such as uncertainty quantification, optimization, or the generation of databases for machine-learning training. Surrogate modeling addresses this issue by approximating the mapping between input parameters and output responses when direct high-fidelity evaluations are too expensive. Stochastic collocation methods are a common example. However, when the number of uncertain parameters increases, the computational cost of standard tensor-product collocation grows exponentially. Sparse grids, originally introduced by Smolyak in 1963, alleviate this curse of dimensionality compared to full tensor grids, but they treat all regions of the parameter space isotropically, which can be inefficient when higher resolution is required only in specific regions.
This work presents a bi-fidelity framework for constructing sparse grid interpolants guided by an error indicator that provides a zero-cost estimate of the hierarchical surplus. The indicator is evaluated at candidate points in the next-level grid $w+1$ not already included in the base grid $w$, by computing the relative difference between the predictions of two consecutive interpolants of level $w$ and $w-1$. Candidate points are ranked according to this metric and only the most impactful ones are selected up to a prescribed budget. The final higher-order model is then built by evaluating the expensive objective function only at these selected points, while the remaining nodes of the $w+1$ grid are assigned the values predicted by the level-$w$ surrogate. The approach is tested on analytical functions and on the sensitivity analysis of flashback in hydrogen-fueled perforated burners with respect to four geometrical parameters. Results show that the proposed framework significantly reduces the error while requiring far fewer DNS evaluations than a fully resolved higher-level sparse grid.