Semi-intrusive uncertainty propagation for multiscale models

Improved Non-Intrusive Uncertainty Propagation in Complex Fluid Flow Problems

The problem of non-intrusive uncertainty quantification is studied, with a focus on two computational fluid dynamics cases. A collocation method using quadrature or cubature rules is applied, where the simulations are selected deterministically. A one-dimensional quadrature rule is proposed which is nested, symmetric, and has positive weights. The rule is based on the removal of nodes from an e...

Nonlinear Propagation of Orbit Uncertainty Using Non-Intrusive Polynomial Chaos

This paper demonstrates the use of polynomial chaos expansions (PCEs) for the nonlinear, non-Gaussian propagation of orbit state uncertainty. Using linear expansions in tensor-products of univariate orthogonal polynomial bases, PCEs approximate the stochastic solution of the ordinary differential equation describing the propagated orbit, and include information on covariance, higher moments, an...

Uncertainty propagation in a multiscale model of nanocrystalline plasticity

We characterize how uncertainties propagate across spatial and temporal scales in a physics-based model of nanocrystalline plasticity of fcc metals. Our model combines molecular dynamics (MD) simulations to characterize atomic-level processes that govern dislocation-based-plastic deformation with a phase field approach to dislocation dynamics (PFDD) that describes how an ensemble of dislocation...

Approximate Methods for Propagation of Uncertainty with Gaussian Process Models

Uncertainty Propagation for Nonlinear Dynamic Systems Using Gaussian Mixture Models

A Gaussian-mixture-model approach is proposed for accurate uncertainty propagation through a general nonlinear system. The transition probability density function is approximated by a finite sum of Gaussian density functions for which the parameters (mean and covariance) are propagated using linear propagation theory. Two different approaches are introduced to update the weights of different co...