Gradient-Free Construction of Active Subspaces for Dimension Reduction
Authors: Brian J. Williams (LANL), Allison Lewis (Johns Hopkins University), Ralph C. Smith (NCSU), Max Morris (ISU), Bassam Khuwaileh (Univ. of Sharjah)
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 low-order 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 talk, we discuss a gradient free active subspace algorithm that is feasible for high-dimensional parameter spaces where finite-difference techniques are impractical. We illustrate an initialized gradient-free active subspace algorithm for a neutronics example implemented with SCALE6.1, for input dimensions up to 7700. We also illustrate the potential for active subspace identification to facilitate sensitivity analysis and model parameter calibration to experimental data.