  Timely completion of design cycles for complex systems ranging from consumer
electronics to hypersonic vehicles relies on rapid simulation-based
prototyping. The latter typically involves high-dimensional spaces of possibly
correlated control variables (CVs) and quantities of interest (QoIs) with
non-Gaussian and possibly multimodal distributions. We develop a
model-agnostic, moment-independent global sensitivity analysis (GSA) that
relies on differential mutual information to rank the effects of CVs on QoIs.
The data requirements of this information-theoretic approach to GSA are met by
replacing computationally intensive components of the physics-based model with
a deep neural network surrogate. Subsequently, the GSA is used to explain the
network predictions, and the surrogate is deployed to close design loops.
Viewed as an uncertainty quantification method for interrogating the surrogate,
this framework is compatible with a wide variety of black-box models. We
demonstrate that the surrogate-driven mutual information GSA provides useful
and distinguishable rankings on two applications of interest in energy storage.
Consequently, our information-theoretic GSA provides an "outer loop" for
accelerated product design by identifying the most and least sensitive input
directions and performing subsequent optimization over appropriately reduced
parameter subspaces.
