  Phase-field modeling is an effective but computationally expensive method for
capturing the mesoscale morphological and microstructure evolution in
materials. Hence, fast and generalizable surrogate models are needed to
alleviate the cost of computationally taxing processes such as in optimization
and design of materials. The intrinsic discontinuous nature of the physical
phenomena incurred by the presence of sharp phase boundaries makes the training
of the surrogate model cumbersome. We develop a framework that integrates a
convolutional autoencoder architecture with a deep neural operator (DeepONet)
to learn the dynamic evolution of a two-phase mixture and accelerate
time-to-solution in predicting the microstructure evolution. We utilize the
convolutional autoencoder to provide a compact representation of the
microstructure data in a low-dimensional latent space. DeepONet, which consists
of two sub-networks, one for encoding the input function at a fixed number of
sensors locations (branch net) and another for encoding the locations for the
output functions (trunk net), learns the mesoscale dynamics of the
microstructure evolution from the autoencoder latent space. The decoder part of
the convolutional autoencoder then reconstructs the time-evolved microstructure
from the DeepONet predictions. The trained DeepONet architecture can then be
used to replace the high-fidelity phase-field numerical solver in interpolation
tasks or to accelerate the numerical solver in extrapolation tasks.
