  Particle accelerators are time-varying systems whose components are perturbed
by external disturbances. Tuning accelerators can be a time-consuming process
involving manual adjustment of multiple components, such as RF cavities, to
minimize beam loss due to time-varying drifts. The high dimensionality of the
system ($\sim$100 amplitude and phase RF settings in the LANSCE accelerator)
makes it difficult to achieve optimal operation. The time-varying drifts and
the dimensionality make system parameter estimation a challenging optimization
problem. In this work, we propose a Variational Autoencoded Latent Regression
(VALeR) model for robust estimation of system parameters using 2D unique
projections of a charged particle beam's 6D phase space. In VALeR, VAE projects
the phase space projections into a lower-dimensional latent space, and a dense
neural network maps the latent space onto the space of system parameters. The
trained network can predict system parameters for unseen phase space
projections. Furthermore, VALeR can generate new projections by randomly
sampling the latent space of VAE and also estimate the corresponding system
parameters.
