  A new generation of phenomenological optical potentials requires robust
calibration and uncertainty quantification, motivating the use of Bayesian
statistical methods. These Bayesian methods usually require calculating
observables for thousands or even millions of parameter sets, making fast and
accurate emulators highly desirable or even essential. Emulating scattering
across different energies or with interactions such as optical potentials is
challenging because of the non-affine parameter dependence, meaning the
parameters do not all factorize from individual operators. Here we introduce
and demonstrate the Reduced Order Scattering Emulator (ROSE) framework, a
reduced basis emulator that can handle non-affine problems. ROSE is fully
extensible and works within the publicly available BAND Framework software
suite for calibration, model mixing, and experimental design. As a
demonstration problem, we use ROSE to calibrate a realistic nucleon-target
scattering model through the calculation of elastic cross sections. This
problem shows the practical value of the ROSE framework for Bayesian
uncertainty quantification with controlled trade-offs between emulator speed
and accuracy as compared to high-fidelity solvers. Planned extensions of ROSE
are discussed.
