  Renewable energy researchers use computer simulation to aid the design of
lithium ion storage devices. The underlying models contain several physical
input parameters that affect model predictions. Effective design and analysis
must understand the sensitivity of model predictions to changes in model
parameters, but global sensitivity analyses become increasingly challenging as
the number of input parameters increases. Active subspaces are part of an
emerging set of tools for discovering and exploiting low-dimensional structures
in the map from high-dimensional inputs to model outputs. We extend linear and
quadratic model-based heuristic for active sub- space discovery to
time-dependent processes and apply the resulting technique to a lithium ion
battery model. The results reveal low-dimensional structure and sensitivity
metrics that a designer may exploit to study the relationship between
parameters and predictions.
