Adaptive tuning of the latent space of encoder-decoder convolutional neural networks for virtual 6D diagnostics of time-varying charged particle beams*

Advanced and future high energy physics facilities, such as the FACET-II beam-driven plasma wakefield accelerator (PWFA), require an ability to generate and accelerate extremely short (few fs) high charge (few nC) high peak current (> 200 kA) electron bunches while maintaing minimal energy spread and precise control of current profiles which is crucial for the PWFA process. We present a novel method of adaptive machine learning (AML) which combines ML techniques such as convolutional neural networks (CNN) with model-independent feedback control theory for time-varying systems. Our encoder-decoder CNN maps high dimensional inputs (128x128 pixel images = 16348 dimensions) to representations in a general nonlinear 2-dimensional latent space, which is then used to generate a 1.2288E6 dimensional output which is all 15 of the unique 2D projections of a charged particle beam's 6D (x,y,z,px,py,E) phase space at 5 different locations in an accelerator (75 128x128 pixel images). Only a single one of the 75 generated projections, the (z,E) longitudinal phase space, is compared to a measurement which provides adaptive feedback acting directly on the low dimensional latent space of the network allowing us to estimate all projections of the beam's 6D phase space as the beam changes with time.