  We propose a novel deep learning based surrogate model for solving
high-dimensional uncertainty quantification and uncertainty propagation
problems. The proposed deep learning architecture is developed by integrating
the well-known U-net architecture with the Gaussian Gated Linear Network (GGLN)
and referred to as the Gated Linear Network induced U-net or GLU-net. The
proposed GLU-net treats the uncertainty propagation problem as an image to
image regression and hence, is extremely data efficient. Additionally, it also
provides estimates of the predictive uncertainty. The network architecture of
GLU-net is less complex with 44\% fewer parameters than the contemporary works.
We illustrate the performance of the proposed GLU-net in solving the Darcy flow
problem under uncertainty under the sparse data scenario. We consider the
stochastic input dimensionality to be up to 4225. Benchmark results are
generated using the vanilla Monte Carlo simulation. We observe the proposed
GLU-net to be accurate and extremely efficient even when no information about
the structure of the inputs is provided to the network. Case studies are
performed by varying the training sample size and stochastic input
dimensionality to illustrate the robustness of the proposed approach.
