We propose a non-intrusive reduced basis (RB) method for parametrized nonlinear partial
differential equations (PDEs) that leverages models of different accuracy. From a collection …

This article first presents a short historical perpective of the importance splitting approach to
simulate and estimate rare events, with a detailed description of several variants. We then …

The estimation of rare event or failure probabilities in high dimensions is of interest in many
areas of science and technology. We consider problems where the rare event is expressed …

Reliability-based design approaches via scenario optimization are driven by data thereby
eliminating the need for creating a probabilistic model of the uncertain parameters. A …

We propose a multifidelity dimension reduction method to identify a low-dimensional
structure present in many engineering models. The structure of interest arises when …

The identification of parameters in mathematical models using noisy observations is a
common task in uncertainty quantification. We employ the framework of Bayesian inversion …

Accurately estimating rare event probabilities with Monte Carlo can become costly if for each
sample a computationally expensive high-fidelity model evaluation is necessary to …

In failure probability estimation, importance sampling constructs a biasing distribution that
targets the failure event such that a small number of model evaluations is sufficient to …

Many applications across sciences and technologies require a careful quantification of
nondeterministic effects to a system output, for example, when evaluating the system's …

We propose a method for the accurate estimation of rare event or failure probabilities for
expensive-to-evaluate numerical models in high dimensions. The proposed approach …