Nonintrusive Polynomial Chaos Expansions for Sensitivity Analysis in Stochastic Differential Equations

DOI10.1137/16M1061989zbMath1367.60091MaRDI QIDQ5269869

Omar M. Knio, M. Navarro Jimenez, Olivier P. Le Maître

Publication date: 28 June 2017

Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)

zbMATH Keywords

stochastic differential equationsvariance decompositionpolynomial chaos expansions

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Algorithms for approximation of functions (65D15) Numerical quadrature and cubature formulas (65D32)

Related Items

Sensitivity Analysis for Stability of Uncertain Delay Differential Equations Using Polynomial Chaos Expansions, Global sensitivity analysis for models described by stochastic differential equations, A spectral surrogate model for stochastic simulators computed from trajectory samples, Emulation of Stochastic Simulators Using Generalized Lambda Models, Model order reduction for random nonlinear dynamical systems and low-dimensional representations for their quantities of interest, 10 Model order reduction in uncertainty quantification

Uses Software

• bootstrap

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Uncertainty propagation using Wiener-Haar expansions
• Multi-resolution analysis of Wiener-type uncertainty propagation schemes
• Monte Carlo algorithms for evaluating Sobol' sensitivity indices
• Sparse pseudospectral approximation method
• Mathematical epidemiology.
• On Latin hypercube sampling
• Dimension-adaptive tensor-product quadrature
• Making best use of model evaluations to compute sensitivity indices
• Stochastic differential equations applied to the study of geophysical and financial time series
• A stochastic projection method for fluid flow. II: Random process
• Wong-Zakai approximations for stochastic differential equations
• The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals
• Non-Gaussian Ornstein–Uhlenbeck-based Models and Some of Their Uses in Financial Economics
• Sparse Quadrature as an Alternative to Monte Carlo for Stochastic Finite Element Techniques
• A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code
• Spectral Methods for Uncertainty Quantification
• A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
• Approximate Integration of Stochastic Differential Equations
• Uncertainty Quantification in CFD Simulations: A Stochastic Spectral Approach
• Sensitivity Analysis in Practice
• Adaptive Anisotropic Spectral Stochastic Methods for Uncertain Scalar Conservation Laws
• Uncertainty Quantification in MD Simulations. Part I: Forward Propagation
• Uncertainty Quantification in MD Simulations. Part II: Bayesian Inference of Force-Field Parameters
• A computable evolution equation for the joint response-excitation probability density function of stochastic dynamical systems
• Adaptive Smolyak Pseudospectral Approximations
• Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates
• Lectures on Monte Carlo methods
• Runge-Kutta methods for numerical solution of stochastic differential equations