  The BUQEYE collaboration (Bayesian Uncertainty Quantification: Errors in Your
EFT) presents a pedagogical introduction to projection-based, reduced-order
emulators for applications in low-energy nuclear physics. The term emulator
refers here to a fast surrogate model capable of reliably approximating
high-fidelity models. As the general tools employed by these emulators are not
yet well-known in the nuclear physics community, we discuss variational and
Galerkin projection methods, emphasize the benefits of offline-online
decompositions, and explore how these concepts lead to emulators for bound and
scattering systems that enable fast & accurate calculations using many
different model parameter sets. We also point to future extensions and
applications of these emulators for nuclear physics, guided by the mature field
of model (order) reduction. All examples discussed here and more are available
as interactive, open-source Python code so that practitioners can readily adapt
projection-based emulators for their own work.
