  The event generator Sar$t$re has been used extensively for simulations of
electron-ion collisions in preparation for the Electron-Ion Collider (EIC).
Sar$t$re simulates exclusive diffraction in $e$A collisions, in principle for
any nuclear species and exclusive final state, usually a vector meson. The
coherent and incoherent cross sections for each process are calculated in the
colour dipole model for small $x$ from the first and second moments of the
respective amplitude, averaged over initial state spatial configurations.
Taking these averages is a very CPU demanding task. In order to function as an
efficient event generator, these amplitude moments are saved into lookup tables
which are used as input for the event generation, making the latter a very fast
process. However, there are many recent and ongoing developments of the dipole
models underlying the calculations, both in terms of fits of the model
parameters to new data as well as new parametrisations of the dipole or proton
geometries. Therefore, it is desirable to have a more flexible method for
producing the lookup tables. Here, we propose a method using neural networks
which can reduce the table production time by 90% while retaining the same
precision in the resulting cross sections.
