Recent developments in the field of reduced-order modeling-and, in particular, active subspace construction-have made it possible to efficiently approximate complex models by constructing loworder response surfaces based upon a small subspace of the original high-dimensional parameter space. These methods rely upon the fact that the response tends to vary more prominently in a few dominant directions defined by linear combinations of the original inputs, allowing for a rotation of the coordinate axis and a consequent transformation of the parameters. In this paper, we discuss a gradient-free active subspace algorithm that is feasible for high-dimensional parameter spaces where finite-difference techniques are impractical. This analysis extends the gradient-free algorithm introduced in [A.

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