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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
Uncertainty Quantification for Fat-Tailed Probability Distributions in Aircraft Engine Simulations
R. Ahlfeld, F. Montomoli, E. Scalas and S. Shahpar Journal of Propulsion and Power 33(4) 881 (2017) https://doi.org/10.2514/1.B36278
Xun Huan, Cosmin Safta, Khachik Sargsyan, Gianluca Geraci, Michael S. Eldred, Zachary Vane, Guilhem Lacaze, Joseph C. Oefelein and Habib N. Najm (2017) https://doi.org/10.2514/6.2017-1089
Arbitrary Polynomial Chaos for Uncertainty Propagation of Correlated Random Variables in Dynamic Systems
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
Generalized polynomial chaos for nonlinear random delay differential equations
A generalized multi-resolution expansion for uncertainty propagation with application to cardiovascular modeling
D.E. Schiavazzi, A. Doostan, G. Iaccarino and A.L. Marsden Computer Methods in Applied Mechanics and Engineering 314 196 (2017) https://doi.org/10.1016/j.cma.2016.09.024
Sparse Adaptive Tensor Galerkin Approximations of Stochastic PDE-Constrained Control Problems
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
A constant phase approach for the frequency response of stochastic linear oscillators
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
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
Fundamental equations with higher order Malliavin operators
Influence of Physical and Geometrical Uncertainties in the Parametric Instability Load of an Axially Excited Cylindrical Shell
Frederico Martins Alves da Silva, Augusta Finotti Brazão and Paulo Batista Gonçalves Mathematical Problems in Engineering 2015 1 (2015) https://doi.org/10.1155/2015/758959
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
Uncertainty quantification in LES of a turbulent bluff-body stabilized flame
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
Quantifying Sampling Noise and Parametric Uncertainty in Atomistic-to-Continuum Simulations Using Surrogate Models
Polynomial Chaos Expansion Approach to Interest Rate Models
Luca Di Persio, Gregorio Pellegrini and Michele Bonollo Journal of Probability and Statistics 2015 1 (2015) https://doi.org/10.1155/2015/369053
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
Marcela Mendoza, Sanggyun Kim and Todd P. Coleman 1270 (2015) https://doi.org/10.1109/GlobalSIP.2015.7418402
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
Computing the Cross-Sectional Distribution to Approximate Stationary Markov Equilibria with Heterogeneous Agents and Incomplete Markets
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
Inverse modeling of geochemical and mechanical compaction in sedimentary basins through Polynomial Chaos Expansion
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
Constructing Nested Nodal Sets for Multivariate Polynomial Interpolation