  The use of QCD calculations that include the resummation of soft-collinear
logarithms via parton-shower algorithms is currently not possible in PDF fits
due to the high computational cost of evaluating observables for each variation
of the PDFs. Unfortunately the interpolation methods that are otherwise applied
to overcome this issue are not readily generalised to all-order parton-shower
contributions. Instead, we propose an approximation based on training a neural
network to predict the effect of varying the input parameters of a parton
shower on the cross section in a given observable bin, interpolating between
the variations of a training data set. This first publication focuses on
providing a proof-of-principle for the method, by varying the shower dependence
on $\alpha_\text{S}$ for both a simplified shower model and a complete shower
implementation for three different observables, the leading emission scale, the
number of emissions and the Thrust event shape. The extension to the PDF
dependence of the initial-state shower evolution that is needed for the
application to PDF fits is left to a forthcoming publication.
