  Understanding the mechanisms of shock-induced pore collapse is of great
interest in various disciplines in sciences and engineering, including
materials science, biological sciences, and geophysics. However, numerical
modeling of the complex pore collapse processes can be costly. To this end, a
strong need exists to develop surrogate models for generating economic
predictions of pore collapse processes. In this work, we study the use of a
data-driven reduced order model, namely dynamic mode decomposition, and a deep
generative model, namely conditional generative adversarial networks, to
resemble the numerical simulations of the pore collapse process at
representative training shock pressures. Since the simulations are expensive,
the training data are scarce, which makes training an accurate surrogate model
challenging. To overcome the difficulties posed by the complex physics
phenomena, we make several crucial treatments to the plain original form of the
methods to increase the capability of approximating and predicting the
dynamics. In particular, physics information is used as indicators or
conditional inputs to guide the prediction. In realizing these methods, the
training of each dynamic mode composition model takes only around 30 seconds on
CPU. In contrast, training a generative adversarial network model takes 8 hours
on GPU. Moreover, using dynamic mode decomposition, the final-time relative
error is around 0.3% in the reproductive cases. We also demonstrate the
predictive power of the methods at unseen testing shock pressures, where the
error ranges from 1.3% to 5% in the interpolatory cases and 8% to 9% in
extrapolatory cases.
