@article{cleaves_alexanderian_saad_2021, title={Structure exploiting methods for fast uncertainty quantification in multiphase flow through heterogeneous media}, ISSN={["1573-1499"]}, DOI={10.1007/s10596-021-10085-8}, abstractNote={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-valued 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-Loéve (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.}, journal={COMPUTATIONAL GEOSCIENCES}, author={Cleaves, Helen and Alexanderian, Alen and Saad, Bilal}, year={2021}, month={Sep} }
 @article{cleaves_alexanderian_guy_smith_yu_2019, title={DERIVATIVE-BASED GLOBAL SENSITIVITY ANALYSIS FOR MODELS WITH HIGH-DIMENSIONAL INPUTS AND FUNCTIONAL OUTPUTS}, volume={41}, ISSN={["1095-7197"]}, DOI={10.1137/19M1243518}, abstractNote={We present a framework for derivative-based global sensitivity analysis (GSA) for models with high-dimensional input parameters and functional outputs. We combine ideas from derivative-based GSA, random field representation via Karhunen--Lo\`{e}ve expansions, and adjoint-based gradient computation to provide a scalable computational framework for computing the proposed derivative-based GSA measures. We illustrate the strategy for a nonlinear ODE model of cholera epidemics and for elliptic PDEs with application examples from geosciences and biotransport.}, number={6}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Cleaves, Helen L. and Alexanderian, Alen and Guy, Hayley and Smith, Ralph C. and Yu, Meilin}, year={2019}, pages={A3524–A3551} }