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Robust Information Divergences for Model-Form Uncertainty Arising from Sparse Data in Random PDE
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A generalized multi-resolution expansion for uncertainty propagation with application to cardiovascular modeling
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Generalized polynomial chaos for nonlinear random delay differential equations
Efficient Uncertainty Quantification in Stochastic Economic Dispatch
Cosmin Safta, Richard L.-Y. Chen, Habib N. Najm, Ali Pinar and Jean-Paul Watson IEEE Transactions on Power Systems 32(4) 2535 (2017) https://doi.org/10.1109/TPWRS.2016.2615334
Stochastic Collocation Methods via $\ell_1$ Minimization Using Randomized Quadratures
Ling Guo, Akil Narayan, Tao Zhou and Yuhang Chen SIAM Journal on Scientific Computing 39(1) A333 (2017) https://doi.org/10.1137/16M1059680
Improving adaptive generalized polynomial chaos method to solve nonlinear random differential equations by the random variable transformation technique
J.-C. Cortés, J.-V. Romero, M.-D. Roselló and R.-J. Villanueva Communications in Nonlinear Science and Numerical Simulation 50 1 (2017) https://doi.org/10.1016/j.cnsns.2017.02.011
Probability of failure sensitivity analysis using polynomial expansion
Cosmin Safta, Myra Blaylock, Jeremy Templeton, et al. International Journal for Numerical Methods in Fluids 83(4) 376 (2017) https://doi.org/10.1002/fld.4272
Inverse uncertainty quantification of reactor simulations under the Bayesian framework using surrogate models constructed by polynomial chaos expansion
Low-rank solvers for unsteady Stokes–Brinkman optimal control problem with random data
Peter Benner, Sergey Dolgov, Akwum Onwunta and Martin Stoll Computer Methods in Applied Mechanics and Engineering 304 26 (2016) https://doi.org/10.1016/j.cma.2016.02.004
Uncertainty quantification in virtual surgery hemodynamics predictions for single ventricle palliation
D. E. Schiavazzi, G. Arbia, C. Baker, A. M. Hlavacek, T. Y. Hsia, A. L. Marsden, I. E. Vignon‐Clementel and The Modeling of Congenital Hearts Alliance (MOCH International Journal for Numerical Methods in Biomedical Engineering 32(3) (2016) https://doi.org/10.1002/cnm.2737
SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos
Wiener–Poisson chaos expansion and numerical solutions of the Heath–Jarrow–Morton interest rate model
Evangelia A. Kalpinelli and Nikolaos E. Frangos Stochastics and Partial Differential Equations: Analysis and Computations 4(2) 361 (2016) https://doi.org/10.1007/s40072-015-0066-6
Subspace inverse power method and polynomial chaos representation for the modal frequency responses of random mechanical systems
Probabilistic Density Function Method for Stochastic ODEs of Power Systems with Uncertain Power Input
P. Wang, D. A. Barajas-Solano, E. Constantinescu, et al. SIAM/ASA Journal on Uncertainty Quantification 3(1) 873 (2015) https://doi.org/10.1137/130940050
Low-Rank Solution of Unsteady Diffusion Equations with Stochastic Coefficients
Peter Benner, Akwum Onwunta and Martin Stoll SIAM/ASA Journal on Uncertainty Quantification 3(1) 622 (2015) https://doi.org/10.1137/130937251
Variational Theory and Computations in Stochastic Plasticity
Quantifying Sampling Noise and Parametric Uncertainty in Atomistic-to-Continuum Simulations Using Surrogate Models
Maher Salloum, Khachik Sargsyan, Reese Jones, Habib N. Najm and Bert Debusschere Multiscale Modeling & Simulation 13(3) 953 (2015) https://doi.org/10.1137/140989601
Analysis of the Ensemble and Polynomial Chaos Kalman Filters in Bayesian Inverse Problems
Oliver G. Ernst, Björn Sprungk and Hans-Jörg Starkloff SIAM/ASA Journal on Uncertainty Quantification 3(1) 823 (2015) https://doi.org/10.1137/140981319
Influence of Physical and Geometrical Uncertainties in the Parametric Instability Load of an Axially Excited Cylindrical Shell
Polynomial Chaos Expansion of a Multimodal Random Vector
C. Soize SIAM/ASA Journal on Uncertainty Quantification 3(1) 34 (2015) https://doi.org/10.1137/140968495
Gabriela Ciuprina, Jorge Fernández Villena, Daniel Ioan, Zoran Ilievski, Sebastian Kula, E. Jan W. ter Maten, Kasra Mohaghegh, Roland Pulch, Wil H. A. Schilders, L. Miguel Silveira, Alexandra Ştefănescu and Michael Striebel 21 267 (2015) https://doi.org/10.1007/978-3-662-46672-8_5
Constructing adaptive generalized polynomial chaos method to measure the uncertainty in continuous models: A computational approach
Preconditioned Bayesian Regression for Stochastic Chemical Kinetics
Alen Alexanderian, Francesco Rizzi, Muruhan Rathinam, Olivier P. Le Maître and Omar M. Knio Journal of Scientific Computing 58(3) 592 (2014) https://doi.org/10.1007/s10915-013-9745-5
Stochastic collocation and stochastic Galerkin methods for linear differential algebraic equations
On the convergence of the stochastic Galerkin method for random elliptic partial differential equations
Antje Mugler and Hans-Jörg Starkloff ESAIM: Mathematical Modelling and Numerical Analysis 47(5) 1237 (2013) https://doi.org/10.1051/m2an/2013066
Wick–Malliavin approximation to nonlinear stochastic partial differential equations: analysis and simulations
D. Venturi, X. Wan, R. Mikulevicius, B. L. Rozovskii and G. E. Karniadakis Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469(2158) 20130001 (2013) https://doi.org/10.1098/rspa.2013.0001
On stability and monotonicity requirements of finite difference approximations of stochastic conservation laws with random viscosity