  Surrogate strategies are used widely for uncertainty quantification of
groundwater models in order to improve computational efficiency. However, their
application to dynamic multiphase flow problems is hindered by the curse of
dimensionality, the saturation discontinuity due to capillarity effects, and
the time-dependence of the multi-output responses. In this paper, we propose a
deep convolutional encoder-decoder neural network methodology to tackle these
issues. The surrogate modeling task is transformed to an image-to-image
regression strategy. This approach extracts high-level coarse features from the
high-dimensional input permeability images using an encoder, and then refines
the coarse features to provide the output pressure/saturation images through a
decoder. A training strategy combining a regression loss and a segmentation
loss is proposed in order to better approximate the discontinuous saturation
field. To characterize the high-dimensional time-dependent outputs of the
dynamic system, time is treated as an additional input to the network that is
trained using pairs of input realizations and of the corresponding system
outputs at a limited number of time instances. The proposed method is evaluated
using a geological carbon storage process-based multiphase flow model with a
2500-dimensional stochastic permeability field. With a relatively small number
of training data, the surrogate model is capable of accurately characterizing
the spatio-temporal evolution of the pressure and discontinuous CO2 saturation
fields and can be used efficiently to compute the statistics of the system
responses.
