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The polynomial chaos approach for reachable set propagation with application to chance‐constrained nonlinear optimal control under parametric uncertainties
Computational uncertainty quantification for random non-autonomous second order linear differential equations via adapted gPC: a comparative case study with random Fröbenius method and Monte Carlo simulation
Improving adaptive generalized polynomial chaos method to solve nonlinear random differential equations by the random variable transformation technique
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Multi-fidelity Gaussian process regression for prediction of random fields
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A generalized multi-resolution expansion for uncertainty propagation with application to cardiovascular modeling
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Inverse uncertainty quantification of reactor simulations under the Bayesian framework using surrogate models constructed by polynomial chaos expansion
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
Polynomial chaos representation of databases on manifolds
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
SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos
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
Dynamical Polynomial Chaos Expansions and Long Time Evolution of Differential Equations with Random Forcing
Local Polynomial Chaos Expansion for Linear Differential Equations with High Dimensional Random Inputs
Yi Chen, John Jakeman, Claude Gittelson and Dongbin Xiu SIAM Journal on Scientific Computing 37(1) A79 (2015) https://doi.org/10.1137/140970100
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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
Algorithms for Propagating Uncertainty Across Heterogeneous Domains
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Parametrization of Random Vectors in Polynomial Chaos Expansions via Optimal Transportation
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
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
Polynomial Chaos Expansion of a Multimodal Random Vector
Analysis of the Ensemble and Polynomial Chaos Kalman Filters in Bayesian Inverse Problems
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Computing the Cross-Sectional Distribution to Approximate Stationary Markov Equilibria with Heterogeneous Agents and Incomplete Markets
Martin Eigel, Claude Jeffrey Gittelson, Christoph Schwab and Elmar Zander Computer Methods in Applied Mechanics and Engineering 270 247 (2014) https://doi.org/10.1016/j.cma.2013.11.015
N-TERM WIENER CHAOS APPROXIMATION RATES FOR ELLIPTIC PDEs WITH LOGNORMAL GAUSSIAN RANDOM INPUTS
Preconditioned Bayesian Regression for Stochastic Chemical Kinetics
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Stochastic collocation and stochastic Galerkin methods for linear differential algebraic equations