Environment for Quantifying Uncertainty:

Integrated aNd Optimized at the eXtreme scale

Sponsored by: DOE - Advanced Scientific Computing Research

- M. Gunzburger, C. Webster, and G. Zhang were invited to write an article “Stochastic finite element methods for partial differential equations with random input data”, published in Acta Numerica, 2014 vol. 23 pp. 521-650., which is the most highly cited journal in mathematics.
- G. Zhang, C. Webster, M. Gunzburger and J. Burkardt were invited to write an article "Hyperspherical Sparse Approximation Techniques for High-Dimensional Discontinuity Detection", published in SIAM Review, 2016 vol. 58(3), pp. 517-551.

- M. Gunzburger and C. Webster were invited to publish a review article "Uncertainty quantification in the partial differential equation setting" in the Springer Mathematical Intelligencer for the Special Issue of the ICIAM16, 2016.
- M. Gunzburger, C. Webster, and G. Zhang were invited to write a chapter on "Sparse collocation methods for stochastic interpolation and quadrature", for the Springer Handbook of Uncertainty Quan- tification, 2016.
- E. Phipps and A. Salinger were invited to write a chapter on "Embedded Uncertainty Quantification Methods via Stokhos", for the Springer Handbook of Uncertainty Quantification, 2016.
- Y. D. Wang and C. F. J. Wu were invited to write a chapter on "Bayesian cubic spline in computer experiments", for the Springer Handbook of Uncertainty Quantification, 2016.
- The book by M. Gunzburger and C. Webster entitled “An algorithmic
introduction to numerical meth- ods for uncertainty quantification for
PDEs with random inputs,” has been selected for publication in the
Spinger Applied Mathematical Sciences, 2016.

- E. Phipps, M. D'Elia, H. C. Edwards, M. Hoemmen, J. Hu, and S. Rajamanickam

Embedded Ensemble Propagation for Improving Performance, Portability and Scalability of Uncertainty Quantification on Emerging Computational Architectures,

Submitted to SIAM Journal on Scientific Computing.

- M. Plumlee, and V. R. Joseph

Orthogonal Gaussian Process Models,

submitted

- R. B. Chen, W. Wang, and C. F. J. Wu

A Bayesian approach for uncertainty quantification in sparse representation surrogate modeling,

submitted

- M. Gunzburger, L. Hou, and J. Ming

Optimal control of stochastic cylinder flow using polynomial chaos expansion,

submitted

- B. Peherstorfer, K. Willcox, and M. Gunzburger

Optimal model management for multifidelity Monte Carlo estimation,

submitted

- H. Tran, C. Webster and G. Zhang

Analysis of quasi-optimal polynomial approximations for parameterized PDEs with deterministic and stochastic coefficients,

submitted to Numerishe Mathematik

- D. Lu, G. Zhang, C. Webster and C. Barbier

Multilevel Monte Carlo method with application to uncertainty quantification in oil reservoir simulation,

submitted to Water Resources Research

- Q. Guan, M. Gunzburger, C. G. Webster, and G. Zhang

Reduced basis methods for nonlocal di usion problems with random input data,

submitted to Computer Methods in Applied Mechanics and Engineering - M. Gunzburger, C. Trenchea, and C. G. Webster,

Error estimates for a sparse interpolation approach to identification and control problems for parameterized stochastic PDEs,

submitted to SIAM Journal on Control and Optimization - P. Jantsch, C. G. Webster, and G. Zhang,

On the Lebesgue constant of weighted Leja points for Lagrange interpolation on unbounded domains,

submitted to Constructive Approximation - A. Chkifa, N. Dexter, H. Tran, and C. G. Webster,

Polynomial approximation via compressed sensing of high- dimensional functions on lower sets,

submitted to Mathematics of Computation

- G. Zhang, C. Webster, M. Gunzburger, and J. Burkardt,

Hyperspherical Sparse Approximation Techniques for High-Dimensional Discontinuity Detection

SIAM Review, Vol. 58, pp. 517-551, 2016.

- F. Bao, Y. Cao, C. Webster and G. Zhang

A meshfree implicit filter for nonlinear filtering problems,

International Journal for Uncertainty Quantification, accepted, to appear in 2016.

- D. Galindo, P. Jantsch, C. Webster and G. Zhang

Accelerating hierarchical stochastic collocation methods for partial differential equations with random input data,

SIAM/ASA Journal on Uncertainty Quantification, accepted, to appear in 2016. - X. He, R. Tuo and C. F. J. Wu

Optimization of computer experiments with tunable accuracy,

to appear in Technometrics. - N. Dexter, C. G. Webster, and G. Zhang,

Explicit cost bounds of stochastic Galerkin approximations for parameterized PDEs with random coefficients

Computers & Mathematics with Applications, vol 71, pp. 2231-2256, 2016. - R. Tuo and C. F. J. Wu

A Thoretical Framework for Calibration in Computer Models: Parametrization, estimation and convergence properties,

SIAM/ASA Journal on Uncertainty Quantification, Vol. 4, pp. 767-795, 2016.

- G. Zhang, W. Zhao, C. G. Webster, and M. Gunzburger

Numerical methods for a class of non- local diffusion problems with the use of backward SDEs,

Comput. Math. Appl., Vol. 71, pp. 2479-2496, 2016.

- M. Gunzburger, L. Hou, and J. Ming

Stochastic steady-state Navier-Stokes equations with additive random noise,

J. Sci. Comput., Vol. 66, pp. 672-691, 2016.

- M. D'Elia, H.C. Edwards, J. Hu, E. Phipps, and S. Rajamanickam

Ensemble Grouping Strategies for Embedded Stochastic Collocation Methods Applied to Anisotropic Diffusion Problems,

SIAM/ASA Journal on Uncertainty Quantification, accepted.

- M. Gunzburger and C. G. Webster

Uncertainty quantification in the partial differential equation setting,

Mathematical Intelligencer Special Issue for ICIAM16; Springer, 2016.

- M. Stoyanov, and C. G. Webster

A Dynamically Adaptive Sparse Grid Method for Quasi-Optimal Interpolation of Multidimensional Analytic Functions,

Computers & Mathematics with Applications, vol 71, pp. 2449-2465, 2016. - V. R. Joseph

Space-filling Designs for Computer Experiments: A Review (with discussions and rejoinder),

Quality Engineering, Vol. 28, pp. 28-44, 2016.

- V. R. Joseph, E. Gul, and S. Ba

Maximum Projection Designs for Computer Experiments,

Biometrika, Vol. 102, pp. 371-380, 2015.

- R. Tuo and C. F. J. Wu

Efficient calibration for imperfect computer models,

Annals of Statistics, Vol. 43, pp. 2331-2352, 2015.

- C. F. J. Wu

Post-Fisherian Experimentation: from Physical to Virtual,

Journal of American Statistical Association, Vol. 110, pp. 612-620, 2015. - M. Stoyanov and C. G. Webster

A gradient-based sampling approach for stochastic dimension reduction for partial di erential equations with random input data,

International Journal for Uncertainty Quantification, Vol. 5, pp. 49-72, 2015. - H.-W. van Wyk, M. Gunzburger, M. Stoyanov, and J. Burkardt

Power-law noises over general spatial domains and on non-standard meshes,

SIAM/ASA J. Uncer. Quant. 3 2015, 296-310.

- G. Zhang, C. G. Webster, M. Gunzburger, J. Burkardt

A hyper-spherical adaptive sparse-grid method for high-dimensional discontinuity detection,

SIAM J. Numer. Anal. 53 2015, 1508-1536.

- A. Teckentrup, P. Jantsch, M. Gunzburger, and C. G. Webster

A multilevel stochastic collocation method for partial differential equations with random input data,

SIAM/ASA J. Uncert. Quant. 3 2015, 1046-1074. - A. Teckentrup and M. Gunzburger

Optimal point sets for total degree polynomial interpolation in moderate dimensions,

arXiv preprint arXiv:1407.3291, 2014.

- Hans-Werner van Wyk, Max Gunzburger, John Burkardt, and Miroslav Stoyanov

Power-Law Noises over General Spatial Domains and on Non-Standard Meshes,

arXiv preprint arXiv:1410.4755, 2014.

- A. Labovsky and M. Gunzburger

An efficient and accurate method for the identification of the most influential random parameters appearing in the input data for PDEs,

SIAM/ASA Journal on Uncertainty Quantification, vol. 2, pages 82-105, 2014. - V. Reshniak, A. Khaliq, D. Voss and G. Zhang

Split-step Milstein methods for multi-channel stiff stochastic differential systems,

Applied Numerical Mathematics, Vol. 89, pp. 1-23, 2015.

- F. Bao, Y. Cao, C. Webster and G. Zhang

A hybrid sparse-grid approach for nonlinear filtering problems based on adaptive-domain of the Zakai equation approximation,

SIAM/ASA Journal on Uncertainty Quantification, Vol. 2(1), pp. 784-804, 2014.

- M. Gunzburger, C. Webster and G. Zhang

Stochastic finite element methods for partial differential equations with random input data,

Acta Numerica, Vol. 23, pp. 521-650, 2014.

- C. G. Webster, G. Zhang and M. Gunzburger

An adaptive sparse-grid-based iterative ensemble Kalman filter approach for parameter field estimation,

International Journal on Computer Mathematics, Vol. 91(4), pp. 798-817, 2014.

- X. Zhang, C. Liu, B. Hu and G. Zhang

Uncertainty analysis of multi-rate kinetics of uranium desorption from sediments,

Journal of Contaminant Hydrology, Vol. 156, pp. 1-15, 2014.

- G. Zhang, D. Lu, M. Ye, M. Gunzburger and C. Webster

An efficient surrogate modeling approach in Bayesian uncertainty analysis,

AIP Conference Proceedings Vol. 1558, pp. 898-901, 2013.

- G. Zhang, D. Lu, M. Ye, M. Gunzburger and C. Webster

An adaptive sparse-grid high-order stochastic collocation method for Bayesian inference in groundwater reactive transport modeling,

Water Resources Research, Vol. 49(10), pp. 6871-6892, 2013.

- G. Zhang, M. Gunzburger and W. Zhao

A sparse-grid method for multi-dimensional backward stochastic differential equations,

Journal of Computational Mathematics, Vol. 31(3), pp. 221-248, 2013.

- C. G. Webster, G. Zhang and M. Gunzburger,

An adaptive sparse-grid iterative ensemble Kalman filter approach for parameter field estimation,

International Journal of Computer Mathematics, 91(4):798-817, 2014. - M. Gunzburger, C. G. Webster, and G. Zhang

Stochastic finite element methods for partial differential equations with random input data,

Acta Numerica, 23:521-650, 5 2014. - J. Dongarra, J. Hittinger, J. Bell, L. Chacon, R. Falgout, M. Heroux, P. Hovland, E. Ng, C. Webster, and S. Wild

Applied mathematics research for exascale computing,

Technical report, Department of Energy, 2013.

- E.Phipps

Embedded Uncertainty Quantification Methods via Stokhos,

Handbook of Uncertainty Quantification, Springer, 2016. - M. Gunzburger, C. G. Webster, and G. Zhang

Sparse collocation methods for stochastic interpolation and quadrature,

Handbook on Uncertainty Quantification, Springer, 2016.

- Y. D. Wang and C. F. J. Wu

Bayesian cubic spline in computer experiments,

Handbook of Uncertainty Quantification, Springer, 2016. - H. Tran, C. Webster and G. Zhang

Bayesian inference for Smagorinsky models in simulating flow around a cylinder at sub-critial reynolds number,

In Sparse Grids and Applications - Sttutgart, volume 109 of Lecture Notes in Computational Science and Engineering, pages 291-313. Springer International Publishing, 2016. - M. Gunzburger, C. G. Webster, and G. Zhang

An adaptive wavelet stochastic collocation method for irregular solutions of partial differential equations with random input data,

In Sparse Grids and Applications - Munich 2012, volume 97 of Lecture Notes in Computational Science and Engineering, pages 137-170. Springer International Publishing, 2014.

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