Polynomial chaos expansions (PCE) are well-suited to quantifying uncertainty in models
parameterized by independent random variables. The assumption of independence leads to …

The notion of a tensor captures three great ideas: equivariance, multilinearity, separability.
But trying to be three things at once makes the notion difficult to understand. We will explain …

This paper proposes a statistical framework to assess the risk of passing a non-signalized
intersection for vehicles. First, an intensity model of the near-accident event is established by …

Multifidelity uncertainty quantification (MF UQ) sampling approaches have been shown to
significantly reduce the variance of statistical estimators while preserving the bias of the …

Recently, the graph-accelerated non-intrusive polynomial chaos (NIPC) method has been
proposed for solving uncertainty quantification (UQ) problems. This method leverages the …

The recently introduced graph-accelerated non-intrusive polynomial chaos (NIPC) method
has shown effectiveness in solving a broad range of uncertainty quantification (UQ) …

Methods such as non-intrusive polynomial chaos (NIPC), and stochastic collocation are
frequently used for uncertainty propagation problems. Particularly for low-dimensional …

We construct cubature methods on scattered data via resampling on the support of known
algebraic cubature formulas, by different kinds of adaptive interpolation (polynomial, RBF …

This paper proposes an innovative framework of modeling the statistical properties of the
near-accident event and pedestrian behavior at non-signalized intersections based on …

Stochastic spectral methods have achieved a great success in the uncertainty quantification
of many engineering problems, including variation-aware electronic and photonic design …