  In this work we employ an encoder-decoder convolutional neural network to
predict the failure locations of porous metal tension specimens based only on
their initial porosities. The process we model is complex, with a progression
from initial void nucleation, to saturation, and ultimately failure. The
objective of predicting failure locations presents an extreme case of class
imbalance since most of the material in the specimens do not fail. In response
to this challenge, we develop and demonstrate the effectiveness of data- and
loss-based regularization methods. Since there is considerable sensitivity of
the failure location to the particular configuration of voids, we also use
variational inference to provide uncertainties for the neural network
predictions. We connect the deterministic and Bayesian convolutional neural
networks at a theoretical level to explain how variational inference
regularizes the training and predictions. We demonstrate that the resulting
predicted variances are effective in ranking the locations that are most likely
to fail in any given specimen.
