This paper reviews the mathematical foundation of the importance sampling technique and
discusses two general classes of methods to construct the importance sampling density (or …

In many situations across computational science and engineering, multiple computational
models are available that describe a system of interest. These different models have varying …

For many systems in science and engineering, the governing differential equation is either
not known or known in an approximate sense. Analyses and design of such systems are …

Many multivariate functions in engineering models vary primarily along a few directions in
the space of input parameters. When these directions correspond to coordinate directions …

This work presents an optimal model management strategy that exploits multifidelity
surrogate models to accelerate the estimation of statistics of outputs of computationally …

Physical phenomena are often described by partial differential equations (PDEs), which
have been traditionally solved using computationally demanding finite element, difference …

This work presents a nonlinear model reduction approach for systems of equations
stemming from the discretization of partial differential equations with nonlinear terms. Our …

It is important to design robust and reliable systems by accounting for uncertainty and
variability in the design process. However, performing optimization in this setting can be …

Very efficient sampling algorithms have been proposed to estimate rare event probabilities,
such as Importance Sampling or Importance Splitting. Even if the number of samples …

Estimating statistics of model outputs with the Monte Carlo method often requires a large
number of model evaluations. This leads to long runtimes if the model is expensive to …