  Many model based scientific and engineering methodologies, such as system
identification, sensitivity analysis, optimization and control, require a large
number of model evaluations. In particular, model based real-time control of
urban water infrastructures and online flood alarm systems require fast
prediction of the network response at different actuation and/or parameter
values. General purpose urban drainage simulators are too slow for this
application. Fast surrogate models, so-called emulators, provide a solution to
this efficiency demand. Emulators are attractive, because they sacrifice
unneeded accuracy in favor of speed. However, they have to be fine-tuned to
predict the system behavior satisfactorily. Also, some emulators fail to
extrapolate the system behavior beyond the training set. Although, there are
many strategies for developing emulators, up until now the selection of the
emulation strategy remains subjective. In this paper, we therefore compare the
performance of two families of emulators for open channel flows in the context
of urban drainage simulators. We compare emulators that explicitly use
knowledge of the simulator's equations, i.e. mechanistic emulators based on
Gaussian Processes, with purely data-driven emulators using matrix
factorization. Our results suggest that in many urban applications, naive
data-driven emulation outperforms mechanistic emulation. Nevertheless, we
discuss scenarios in which we think that mechanistic emulation might be
favorable for i) extrapolation in time and ii) dealing with sparse and unevenly
sampled data. We also provide many references to advances in the field of
Machine Learning that have not yet permeated into the Bayesian environmental
science community.
