Changqing Wang

Ilona Ambartsumyan, Eldar Khattatov, ChangQing Wang et al.

Three algorithms are developed for uncertainty quantification in modeling coupled Stokes and Darcy flows. The porous media may consist of multiple regions with different properties. The permeability is modeled as a non-stationary stochastic variable, with its log represented as a sum of local Karhunen-Loève (KL) expansions. The problem is approximated by stochastic collocation on either tensor-product or sparse grids, coupled with a multiscale mortar mixed finite element method for the spatial discretization. A non-overlapping domain decomposition algorithm reduces the global problem to a coarse scale mortar interface problem, which is solved by an iterative solver, for each stochastic realization. In the traditional implementation, each subdomain solves a local Dirichlet or Neumann problem in every interface iteration. To reduce this cost, two additional algorithms based on deterministic or stochastic multiscale flux basis are introduced. The basis consists of the local flux (or velocity trace) responses from each mortar degree of freedom. It is computed by each subdomain independently before the interface iteration begins. The use of the multiscale flux basis avoids the need for subdomain solves on each iteration. The deterministic basis is computed at each stochastic collocation and used only at this realization. The stochastic basis is formed by further looping over all local realizations of a subdomain's KL region before the stochastic collocation begins. It is reused over multiple realizations. Numerical tests are presented to illustrate the performance of the three algorithms, with the stochastic multiscale flux basis showing significant savings in computational cost.

Hao Wang, Qingxuan Wang, Yue Li et al.

The use of visually-rich documents (VRDs) in various fields has created a demand for Document AI models that can read and comprehend documents like humans, which requires the overcoming of technical, linguistic, and cognitive barriers. Unfortunately, the lack of appropriate datasets has significantly hindered advancements in the field. To address this issue, we introduce \textsc{DocTrack}, a VRD dataset really aligned with human eye-movement information using eye-tracking technology. This dataset can be used to investigate the challenges mentioned above. Additionally, we explore the impact of human reading order on document understanding tasks and examine what would happen if a machine reads in the same order as a human. Our results suggest that although Document AI models have made significant progress, they still have a long way to go before they can read VRDs as accurately, continuously, and flexibly as humans do. These findings have potential implications for future research and development of Document AI models. The data is available at \url{https://github.com/hint-lab/doctrack}.