Efficient control variates for uncertainty quantification of radiation transport

Robust Grid Adaptation for Efficient Uncertainty Quantification

In the recent past, adjoint methods have been successfully applied in error estimation of integral outputs (functionals) of the numerical solution of partial differential equations. The adjoint solution can also be used as a grid adaptation indicator, with the objective of optimally targeting and reducing the numerical error in the functional of interest below a prespecified threshold. In situa...

Efficient Sequential Monte Carlo With Multiple Proposals and Control Variates

Sequential Monte Carlo is a useful simulation-based method for online filtering of state-space models. For certain complex state-space models, a single proposal distribution is usually not satisfactory and using multiple proposal distributions is a general approach to address various aspects of the filtering problem. This article proposes an efficient method of using multiple proposals in combi...

An Efficient Computational Framework for Uncertainty Quantification in Multiscale Systems

Efficient Uncertainty Quantification with Polynomial Chaos for Implicit Stiff Systems

The polynomial chaos method has been widely adopted as a computationally feasible approach for uncertainty quantification. Most studies to date have focused on non-stiff systems. When stiff systems are considered, implicit numerical integration requires the solution of a nonlinear system of equations at every time step. Using the Galerkin approach, the size of the system state increases from n ...

An Efficient MCMC Method for Uncertainty Quantification in Inverse Problems

The connection between Bayesian statistics and the technique of regularization for inverse problems has been given significant attention in recent years. For example, Bayes’ law is frequently used as motivation for variational regularization methods of Tikhonov type. In this setting, the regularization function corresponds to the negative-log of the prior probability density; the fit-to-data fu...