Multi-scale control variate methods for uncertainty quantification in kinetic equations

Uncertainty Quantification for Kinetic Equations

Kinetic equations contain uncertainties in their collision kernels or scattering coefficients, initial or boundary data, forcing terms, geometry, etc. Quantifying the uncertainties in kinetic models have important engineering and industrial applications. In this article we survey recent efforts in the study of kinetic equations with random inputs, including their mathematical properties such as...

Scalable Methods for Kinetic Equations

Scalable Methods for Kinetic Equations

Bayesian Solution Uncertainty Quantification for Differential Equations

We explore probability modelling of discretization uncertainty for system states defined implicitly by ordinary or partial differential equations. Accounting for this uncertainty can avoid posterior under-coverage when likelihoods are constructed from a coarsely discretized approximation to system equations. A formalism is proposed for inferring a fixed but a priori unknown model trajectory thr...

Reduced order methods for uncertainty quantification problems

This work provides a review on reduced order methods in solving uncertainty quantification problems. A quick introduction of the reduced order methods, including proper orthogonal decomposition and greedy reduced basis methods, are presented along with the essential components of general greedy algorithm, a posteriori error estimation and Offline-Online decomposition. More advanced reduced orde...