  We propose a novel \textit{capsule} based deep encoder-decoder model for
surrogate modeling and uncertainty quantification of systems in mechanics from
sparse data. The proposed framework is developed by adapting Capsule Network
(CapsNet) architecture into image-to-image regression encoder-decoder network.
Specifically, the aim is to exploit the benefits of CapsNet over convolution
neural network (CNN) $-$ retaining pose and position information related to an
entity to name a few. The performance of proposed approach is illustrated by
solving an elliptic stochastic partial differential equation (SPDE), which also
governs systems in mechanics such as steady heat conduction, ground water flow
or other diffusion processes, based uncertainty quantification problem with an
input dimensionality of $1024$. However, the problem definition does not the
restrict the random diffusion field to a particular covariance structure, and
the more strenuous task of response prediction for an arbitrary diffusion field
is solved. The obtained results from performance evaluation indicate that the
proposed approach is accurate, efficient, and robust.
