  Simulations of thin film sputter deposition require the separation of the
plasma and material transport in the gas-phase from the growth/sputtering
processes at the bounding surfaces. Interface models based on analytic
expressions or look-up tables inherently restrict this complex interaction to a
bare minimum. A machine learning model has recently been shown to overcome this
remedy for Ar ions bombarding a Ti-Al composite target. However, the chosen
network structure (i.e., a multilayer perceptron) provides approximately 4
million degrees of freedom, which bears the risk of overfitting the relevant
dynamics and complicating the model to an unreliable extend. This work proposes
a conceptually more sophisticated but parameterwise simplified regression
artificial neural network for an extended scenario, considering a variable
instead of a single fixed Ti-Al stoichiometry. A convolutional
$\beta$-variational autoencoder is trained to reduce the high-dimensional
energy-angular distribution of sputtered particles to a latent space
representation of only two components. In addition to a primary decoder which
is trained to reconstruct the input energy-angular distribution, a secondary
decoder is employed to reconstruct the mean energy of incident Ar ions as well
as the present Ti-Al composition. The mutual latent space is hence conditioned
on these quantities. The trained primary decoder of the variational autoencoder
network is subsequently transferred to a regression network, for which only the
mapping to the particular latent space has to be learned. While obtaining a
competitive performance, the number of degrees of freedom is drastically
reduced to 15,111 and 486 parameters for the primary decoder and the remaining
regression network, respectively. The underlying methodology is general and can
easily be extended to more complex physical descriptions with a minimal amount
of data required.
