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Multilevel Adaptive Stochastic Collocation with Dimensionality Reduction
2018We present a multilevel stochastic collocation (MLSC) with a dimensionality reduction approach to quantify the uncertainty in computationally intensive applications. Standard MLSC typically employs grids with predetermined resolutions. Even more, stochastic dimensionality reduction has not been considered in previous MLSC formulations.
Ionuţ-Gabriel Farcaş +4 more
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Collocation methods for nonlinear stochastic Volterra integral equations
Computational and Applied Mathematics, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiaoli Xu, Yu Xiao, Haiying Zhang
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Adjoint Error Estimation for Stochastic Collocation Methods
2014This paper deals with partial differential equations with random input data. An efficient way of solving such problems is adaptive stochastic collocation on sparse grids. For higher efficiency and a better understanding of the method, we derive adjoint error estimates for nonlinear stochastic solution functionals.
Bettina Schieche, Jens Lang
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Computational Aspects of Stochastic Collocation with Multifidelity Models
SIAM/ASA Journal on Uncertainty Quantification, 2014In this paper we discuss a numerical approach for the stochastic collocation method with multifidelity simulation models. The method we consider was recently proposed in [A. Narayan, C. Gittelson, and D. Xiu, SIAM J. Sci. Comput., 36 (2014), pp. A495--A521] to combine the computational efficiency of low-fidelity models with the high accuracy of high ...
Xueyu Zhu, Akil Narayan, Dongbin Xiu
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Stochastic optimization using a sparse grid collocation scheme
Probabilistic Engineering Mechanics, 2009Abstract In computational sciences, optimization problems are frequently encountered in solving inverse problems for computing system parameters based on data measurements at specific sensor locations, or to perform design of system parameters. This task becomes increasingly complicated in the presence of uncertainties in boundary conditions or ...
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Application of collocation method to stochastic conservation laws
2017In this chapter we demonstrate how to apply the methods we presented in the previous chapters to stochastic nonlinear conservations laws. Specifically, since the problem is nonlinear we apply the stochastic collocation method (SCM) using Smolyak’s sparse grid for a one-dimensional piston problem and test its computational performance.
Zhongqiang Zhang, George Em Karniadakis
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Stochastic Reachability Analysis using Sparse-Collocation Method
AIAA SCITECH 2023 Forum, 2023Amit Jain, Puneet Singla
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Stochastic Collocation Method for Uncertainty Propagation
AIAA Guidance, Navigation, and Control Conference, 2012Bin Jia, Sheng Cai, Yang Cheng, Ming Xin
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Applications of Stochastic Collocation Method in Electromagnetic Compatibility
2017The paper reviews the use of deterministic-stochastic models in some electromagnetic compatibility (EMC) applications where the uncertainty in input data set exists. In other words, of interest are cases where some properties of a system are partly or entirely unknown.
Poljak, Dragan +4 more
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Evaluation of Designed Distributions for Stochastic Collocation Methods
AIAA SCITECH 2023 Forum, 2023Edwin E. Forster +2 more
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