  We present a computational framework for dimension reduction and surrogate
modeling to accelerate uncertainty quantification in computationally intensive
models with high-dimensional inputs and function-valued outputs. Our driving
application is multiphase flow in saturated-unsaturated porous media in the
context of radioactive waste storage. For fast input dimension reduction, we
utilize an approximate global sensitivity measure, for function-value outputs,
motivated by ideas from the active subspace methods. The proposed approach does
not require expensive gradient computations. We generate an efficient surrogate
model by combining a truncated Karhunen-Lo\'{e}ve (KL) expansion of the output
with polynomial chaos expansions, for the output KL modes, constructed in the
reduced parameter space. We demonstrate the effectiveness of the proposed
surrogate modeling approach with a comprehensive set of numerical experiments,
where we consider a number of function-valued (temporally or spatially
distributed) QoIs.
