  Calibration of the uncertain Arrhenius diffusion parameters for quantifying
mixing rates in Zr-Al nanolaminate foils was performed in a Bayesian setting
[Vohra et al., 2014]. The parameters were inferred in a low temperature regime
characterized by homogeneous ignition and a high temperature regime
characterized by self-propagating reactions in the multilayers. In this work,
we extend the analysis to find optimal experimental designs that would provide
the best data for inference. We employ a rigorous framework that quantifies the
expected in- formation gain in an experiment, and find the optimal design
conditions using numerical techniques of Monte Carlo, sparse quadrature, and
polynomial chaos surrogates. For the low temperature regime, we find the
optimal foil heating rate and pulse duration, and confirm through simulation
that the optimal design indeed leads to sharper posterior distributions of the
diffusion parameters. For the high temperature regime, we demonstrate potential
for increase in the expected information gain of the posteriors by increasing
sample size and reducing uncertainty in measurements. Moreover, posterior
marginals are also produced to verify favorable experimental scenarios for this
regime.
