  In many situations across computational science and engineering, multiple
computational models are available that describe a system of interest. These
different models have varying evaluation costs and varying fidelities.
Typically, a computationally expensive high-fidelity model describes the system
with the accuracy required by the current application at hand, while
lower-fidelity models are less accurate but computationally cheaper than the
high-fidelity model. Outer-loop applications, such as optimization, inference,
and uncertainty quantification, require multiple model evaluations at many
different inputs, which often leads to computational demands that exceed
available resources if only the high-fidelity model is used. This work surveys
multifidelity methods that accelerate the solution of outer-loop applications
by combining high-fidelity and low-fidelity model evaluations, where the
low-fidelity evaluations arise from an explicit low-fidelity model (e.g., a
simplified physics approximation, a reduced model, a data-fit surrogate, etc.)
that approximates the same output quantity as the high-fidelity model. The
overall premise of these multifidelity methods is that low-fidelity models are
leveraged for speedup while the high-fidelity model is kept in the loop to
establish accuracy and/or convergence guarantees. We categorize multifidelity
methods according to three classes of strategies: adaptation, fusion, and
filtering. The paper reviews multifidelity methods in the outer-loop contexts
of uncertainty propagation, inference, and optimization.
